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THORALF SKOLEM

  • Thoralf Skolem
  • Norwegian mathematician

    Thoralf Albert Skolem (Norwegian: [ˈtûːrɑɫf ˈskûːlɛm]; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic, set

    Thoralf Skolem

    Thoralf Skolem

    Thoralf_Skolem

  • Löwenheim–Skolem theorem
  • Existence and cardinality of models of logical theories

    the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation

    Löwenheim–Skolem theorem

    Löwenheim–Skolem_theorem

  • Skolem's paradox
  • Mathematical logic concept

    uncountable set. The paradox arises from part of the Löwenheim–Skolem theorem; Thoralf Skolem was the first to discuss the seemingly contradictory aspects

    Skolem's paradox

    Skolem's paradox

    Skolem's_paradox

  • Skolem normal form
  • Formalism of first-order logic

    Skolem normal form if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may be converted into Skolem

    Skolem normal form

    Skolem_normal_form

  • Skolem arithmetic
  • Mathematical logic

    Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature of Skolem arithmetic

    Skolem arithmetic

    Skolem_arithmetic

  • Skolem–Mahler–Lech theorem
  • The zeros of a linear recurrence relation mostly form a regularly repeating pattern

    zero form a regularly repeating pattern. This result is named after Thoralf Skolem (who proved the theorem for sequences of rational numbers), Kurt Mahler

    Skolem–Mahler–Lech theorem

    Skolem–Mahler–Lech_theorem

  • Thoralf
  • Name list

    in Economic History Thoralf Sandaker (born 1923), Norwegian former rower who competed in the 1948 Summer Olympics Thoralf Skolem (1887–1963), Norwegian

    Thoralf

    Thoralf

  • Russell's paradox
  • Paradox in set theory

    the logical language itself. The language of ZFC, with the help of Thoralf Skolem, turned out to be that of first-order logic. The paradox had already

    Russell's paradox

    Russell's_paradox

  • Skolem–Noether theorem
  • Theorem characterizing the automorphisms of simple rings

    theory of central simple algebras. The theorem was first published by Thoralf Skolem in 1927 in his paper Zur Theorie der assoziativen Zahlensysteme (German:

    Skolem–Noether theorem

    Skolem–Noether_theorem

  • Skolem problem
  • Unsolved problem in mathematics

    values F(0) = 0 and F(1) = 1. The Skolem problem is named after Thoralf Skolem, because of his 1933 paper proving the Skolem–Mahler–Lech theorem on the zeros

    Skolem problem

    Skolem_problem

  • Timeline of mathematical logic
  • called S3. 1920 - Thoralf Skolem proves the (downward) Löwenheim-Skolem theorem using the axiom of choice explicitly. 1922 - Thoralf Skolem proves a weaker

    Timeline of mathematical logic

    Timeline_of_mathematical_logic

  • Primitive recursive arithmetic
  • Formalization of the natural numbers

     289–299. MR 0124194. Archived from the original (PDF) on 10 May 2017. Skolem, Thoralf (1923). "Begründung der elementaren Arithmetik durch die rekurrierende

    Primitive recursive arithmetic

    Primitive_recursive_arithmetic

  • Axiom schema of replacement
  • Concept in set theory

    theory (ZFC). The axiom was independently discovered and announced by Thoralf Skolem later in the same year (and published in 1923). Zermelo himself incorporated

    Axiom schema of replacement

    Axiom_schema_of_replacement

  • Ernst Zermelo
  • German logician and mathematician (1871–1953)

    original axioms, and the original numbering. In 1922, Abraham Fraenkel and Thoralf Skolem independently expanded Zermelo's axiom system, adding the axioms of

    Ernst Zermelo

    Ernst Zermelo

    Ernst_Zermelo

  • Zermelo–Fraenkel set theory
  • Standard system of axiomatic set theory

    property, whose operational meaning was not clear. In 1922, Fraenkel and Thoralf Skolem independently proposed operationalizing a "definite" property as one

    Zermelo–Fraenkel set theory

    Zermelo–Fraenkel set theory

    Zermelo–Fraenkel_set_theory

  • Non-standard model of arithmetic
  • Model of (first-order) Peano arithmetic that contains non-standard numbers

    outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). Non-standard models of arithmetic exist only for the first-order

    Non-standard model of arithmetic

    Non-standard_model_of_arithmetic

  • Zermelo set theory
  • System of mathematical set theory

    of replacement was first published in 1922 by Abraham Fraenkel and Thoralf Skolem, who had independently discovered that Zermelo's axioms cannot prove

    Zermelo set theory

    Zermelo_set_theory

  • Paradoxes of set theory
  • German mathematician Leopold Löwenheim (1915) the Norwegian logician Thoralf Skolem showed in 1922 that every consistent theory of first-order predicate

    Paradoxes of set theory

    Paradoxes_of_set_theory

  • Principle of explosion
  • Theorem in formal logic

    Mathematicians such as Gottlob Frege, Ernst Zermelo, Abraham Fraenkel, and Thoralf Skolem put much effort into revising set theory to eliminate these contradictions

    Principle of explosion

    Principle_of_explosion

  • Morse–Kelley set theory
  • System of mathematical set theory

    Kelley said the system in his book was a variant of the systems due to Thoralf Skolem and Morse. Morse's own version appeared later in his book A Theory of

    Morse–Kelley set theory

    Morse–Kelley_set_theory

  • Continuum hypothesis
  • Proposition in mathematical logic

    generalized continuum hypothesis by Alfred Tarski in 1925. In 1923, Thoralf Skolem conjectured that CH could not be settled by the axioms of Zermelo set

    Continuum hypothesis

    Continuum_hypothesis

  • Axiom schema of specification
  • Concept in axiomatic set theory

    itself a set. The preceding form of separation was introduced in 1930 by Thoralf Skolem as a refinement of a previous, non-first-order form by Zermelo. The

    Axiom schema of specification

    Axiom_schema_of_specification

  • Mathematical logic
  • Subfield of mathematics

    independence results in set theory. Leopold Löwenheim and Thoralf Skolem obtained the Löwenheim–Skolem theorem, which says that first-order logic cannot control

    Mathematical logic

    Mathematical_logic

  • Axiom of choice
  • Axiom of set theory

    Boolean prime ideal theorem; see the section "Weaker forms" below. Löwenheim–Skolem theorem: If a first-order theory has an infinite model, then it has an infinite

    Axiom of choice

    Axiom of choice

    Axiom_of_choice

  • Singleton (mathematics)
  • Set with exactly one element

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Singleton (mathematics)

    Singleton_(mathematics)

  • Uncountable set
  • Infinite set that is not countable

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Uncountable set

    Uncountable_set

  • Complement (set theory)
  • Set of the elements not in a given subset

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Complement (set theory)

    Complement (set theory)

    Complement_(set_theory)

  • Model theory
  • Area of mathematical logic

    downward Löwenheim–Skolem theorem, published by Leopold Löwenheim in 1915. The compactness theorem was implicit in work by Thoralf Skolem, but it was first

    Model theory

    Model_theory

  • Tuple
  • Finite ordered list of elements

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Tuple

    Tuple

  • Turing's proof
  • Proof by Alan Turing

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Turing's proof

    Turing's_proof

  • Axiom of limitation of size
  • Possible axiom of set theory

    his proof of the well-ordering theorem. In 1922, Abraham Fraenkel and Thoralf Skolem pointed out that Zermelo's axioms cannot prove the existence of the

    Axiom of limitation of size

    Axiom of limitation of size

    Axiom_of_limitation_of_size

  • Element of a set
  • Any one of the distinct objects that make up a set in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Element of a set

    Element_of_a_set

  • Computable set
  • Set with algorithmic membership test

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Computable set

    Computable_set

  • Georg Cantor
  • Mathematician (1845–1918)

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Georg Cantor

    Georg Cantor

    Georg_Cantor

  • Øystein Ore
  • Norwegian mathematician (1899–1968)

    a thesis titled Zur Theorie der algebraischen Körper, supervised by Thoralf Skolem. Ore also studied at Göttingen University, where he learned Emmy Noether's

    Øystein Ore

    Øystein Ore

    Øystein_Ore

  • Intersection (set theory)
  • Set of elements common to all of some sets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Intersection (set theory)

    Intersection (set theory)

    Intersection_(set_theory)

  • Empty set
  • Mathematical set containing no elements

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Empty set

    Empty set

    Empty_set

  • Automated theorem proving
  • Subfield of automated reasoning and mathematical logic

    process to automation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the

    Automated theorem proving

    Automated_theorem_proving

  • Set (mathematics)
  • Collection of mathematical objects

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Set (mathematics)

    Set (mathematics)

    Set_(mathematics)

  • Cardinality
  • Size of a set in mathematics

    not a true contradiction in mathematics, was first given in 1922 by Thoralf Skolem, who asserted it as a reason against founding mathematics on first order

    Cardinality

    Cardinality

    Cardinality

  • Ordinal number
  • Generalization of "n-th" to infinite cases

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Ordinal number

    Ordinal number

    Ordinal_number

  • Union (set theory)
  • Set of elements in any of some sets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Union (set theory)

    Union (set theory)

    Union_(set_theory)

  • Burali-Forti paradox
  • Paradox in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Burali-Forti paradox

    Burali-Forti_paradox

  • Cardinal number
  • Size of a possibly infinite set

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Cardinal number

    Cardinal number

    Cardinal_number

  • Class (set theory)
  • Collection of sets in mathematics that can be defined based on a property of its members

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Class (set theory)

    Class_(set_theory)

  • Power set
  • Mathematical set of all subsets of a set

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Power set

    Power set

    Power_set

  • Infinitesimal
  • Extremely small quantity in calculus; thing so small that there is no way to measure it

    Émile Borel and Thoralf Skolem. Borel explicitly linked du Bois-Reymond's work to Cauchy's work on rates of growth of infinitesimals. Skolem developed the

    Infinitesimal

    Infinitesimal

    Infinitesimal

  • Herbrandization
  • Proof of Herbrand's theorem

    formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the Löwenheim–Skolem theorem (Skolem 1920).

    Herbrandization

    Herbrandization

  • Tarski–Grothendieck set theory
  • System of mathematical set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Tarski–Grothendieck set theory

    Tarski–Grothendieck_set_theory

  • Langford pairing
  • Sequence of integers

    "Perfect Skolem sets", Discrete Mathematics, 308 (9): 1653–1664, arXiv:math/0506155, doi:10.1016/j.disc.2006.12.003, MR 2392605. Skolem, Thoralf (1957)

    Langford pairing

    Langford pairing

    Langford_pairing

  • Robert Shostak
  • American computer scientist

    through his collaboration with Kenneth Kunen. Shostak received the Thoralf Skolem Award for "Deciding Combinations of Theories" Shostak is a brother of

    Robert Shostak

    Robert Shostak

    Robert_Shostak

  • Kurt Gödel
  • Mathematician and philosopher (1906–1978)

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Kurt Gödel

    Kurt Gödel

    Kurt_Gödel

  • Almost
  • Term in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Almost

    Almost

  • Large cardinal
  • Set theory concept

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Large cardinal

    Large cardinal

    Large_cardinal

  • Axiom of dependent choice
  • Weak form of the axiom of choice

    {\displaystyle \Rightarrow } Löwenheim–Skolem theorem" — that is, D C {\displaystyle {\mathsf {DC}}} implies the Löwenheim–Skolem theorem. See table Moore, Gregory

    Axiom of dependent choice

    Axiom_of_dependent_choice

  • Transitive set
  • Class of mathematical set whose elements are all subsets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Transitive set

    Transitive_set

  • Subset
  • Set whose elements all belong to another set

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Subset

    Subset

    Subset

  • Norway
  • Country in northern Europe

    plane, laying the foundation for modern vector and complex analysis. Thoralf Skolem made revolutionary contributions to mathematical logic, while Øystein

    Norway

    Norway

    Norway

  • Finite set
  • Finite collection of distinct objects

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Finite set

    Finite set

    Finite_set

  • Axel Thue
  • Norwegian mathematician (1863–1922)

    closely related to the halting problem. His only known PhD student was Thoralf Skolem. The esoteric programming language Thue is named after him. Thue, A

    Axel Thue

    Axel Thue

    Axel_Thue

  • Paul Cohen
  • American mathematician (1934–2007)

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Paul Cohen

    Paul_Cohen

  • Naive set theory
  • Informal set theories

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Naive set theory

    Naive_set_theory

  • 1963
  • Calendar year

    (b. 1907) Mihály Székely, Hungarian bass singer (b. 1901) March 23 – Thoralf Skolem, Norwegian mathematician (b. 1887) March 25 – Felix Adler, American

    1963

    1963

    1963

  • Axiom of extensionality
  • Axiom used in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Axiom of extensionality

    Axiom_of_extensionality

  • General set theory
  • System of mathematical set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    General set theory

    General_set_theory

  • Countable set
  • Mathematical set that can be enumerated

    is a minimal standard model (see Constructible universe). The Löwenheim–Skolem theorem can be used to show that this minimal model is countable. The fact

    Countable set

    Countable_set

  • Venn diagram
  • Diagram that shows all possible logical relations between a collection of sets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Venn diagram

    Venn diagram

    Venn_diagram

  • Schröder–Bernstein theorem
  • Theorem in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Schröder–Bernstein theorem

    Schröder–Bernstein_theorem

  • Gödel logic
  • intuitionistic propositional logic. Intermediate logic von Plato, Jan (2003). "Skolem's Discovery of Gödel-Dummett Logic". Studia Logica. 73 (1): 153–157. doi:10

    Gödel logic

    Gödel_logic

  • List of Norwegian mathematicians
  • being Abel's teacher and tutor, Sophus Lie, Idun Reiten, Atle Selberg, Thoralf Skolem and Carl Størmer. "Aa" appears under "å" as they are considered different

    List of Norwegian mathematicians

    List_of_Norwegian_mathematicians

  • History of mathematical notation
  • Origin and evolution of the symbols used to write equations and formulas

    1921 in "Zum Unitätsproblem der Physik". In 1922, Abraham Fraenkel and Thoralf Skolem independently proposed replacing the axiom schema of specification with

    History of mathematical notation

    History_of_mathematical_notation

  • Fuzzy set
  • Sets whose elements have degrees of membership

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Fuzzy set

    Fuzzy_set

  • Finitism
  • Philosophy of mathematics that accepts only finite objects

    meaningful. The mathematical theory often associated with finitism is Thoralf Skolem's primitive recursive arithmetic. The introduction of infinite mathematical

    Finitism

    Finitism

  • Non-well-founded set theory
  • Theory that allows sets to be elements of themselves

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Non-well-founded set theory

    Non-well-founded_set_theory

  • Bijection
  • One-to-one correspondence

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Bijection

    Bijection

    Bijection

  • Constructible universe
  • Particular class of sets which can be described entirely in terms of simpler sets

    This set is called the minimal model of ZFC. Using the downward Löwenheim–Skolem theorem, one can show that the minimal model (if it exists) is a countable

    Constructible universe

    Constructible_universe

  • Set theory
  • Branch of mathematics that studies sets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Set theory

    Set theory

    Set_theory

  • Set-builder notation
  • Use of braces for specifying sets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Set-builder notation

    Set-builder_notation

  • Regular cardinal
  • Type of cardinal number in mathematics

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Regular cardinal

    Regular_cardinal

  • Metalogic
  • Study of the properties of logical systems

    first-order theories with an infinite model, Löwenheim–Skolem theorem (Leopold Löwenheim 1915 and Thoralf Skolem 1919) Proof of the cut-elimination theorem for

    Metalogic

    Metalogic

  • Algebraic logic
  • Reasoning about equations with free variables

    mathematics, and philosophy. Some writings by Leopold Löwenheim and Thoralf Skolem on algebraic logic appeared after the 1910–13 publication of Principia

    Algebraic logic

    Algebraic_logic

  • List of International Congresses of Mathematicians Plenary and Invited Speakers
  • Siddiqui Carl Ludwig Siegel Waclaw Sierpinski Avadhesh Narayan Singh Thoralf Albert Skolem Virgil Snyder Andreas Speiser Otto Spiess [de] Carl Størmer Wolfgang

    List of International Congresses of Mathematicians Plenary and Invited Speakers

    List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers

  • Axiom schema
  • Template that specifies one or more axioms

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Axiom schema

    Axiom schema

    Axiom_schema

  • Cantor's first set theory article
  • First article on transfinite set theory

    from 1899 to 1901. Countable models are used in set theory. In 1922, Thoralf Skolem proved that if conventional axioms of set theory are consistent, then

    Cantor's first set theory article

    Cantor's first set theory article

    Cantor's_first_set_theory_article

  • Ordered pair
  • Pair of mathematical objects

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Ordered pair

    Ordered pair

    Ordered_pair

  • Axiom of countable choice
  • Concept in mathematics

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Axiom of countable choice

    Axiom of countable choice

    Axiom_of_countable_choice

  • Cantor's diagonal argument
  • Proof in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Cantor's diagonal argument

    Cantor's diagonal argument

    Cantor's_diagonal_argument

  • Equivalence class
  • Mathematical concept

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Equivalence class

    Equivalence class

    Equivalence_class

  • Von Neumann universe
  • Set theory concept

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Von Neumann universe

    Von_Neumann_universe

  • Cantor's paradox
  • Paradox in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Cantor's paradox

    Cantor's_paradox

  • Richard Dedekind
  • German mathematician (1831–1916)

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Richard Dedekind

    Richard Dedekind

    Richard_Dedekind

  • Universal set
  • Mathematical set containing all objects

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Universal set

    Universal_set

  • Peano axioms
  • Axioms for the natural numbers

    Kaye 1991, pp. 16–18. Hermes 1973, VI.4.3, presenting a theorem of Thoralf Skolem Hermes 1973, VI.3.1. Kaye 1991, Section 11.3. Kaye 1991, pp. 70ff..

    Peano axioms

    Peano_axioms

  • Axiom of power set
  • Concept in axiomatic set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Axiom of power set

    Axiom of power set

    Axiom_of_power_set

  • Axiom of determinacy
  • Possible axiom for set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Axiom of determinacy

    Axiom_of_determinacy

  • Infinite set
  • Set that is not a finite set

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Infinite set

    Infinite set

    Infinite_set

  • Axiom of global choice
  • Axiom in set theory

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Axiom of global choice

    Axiom_of_global_choice

  • Paul Bernays
  • Swiss mathematician (1888–1977)

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Paul Bernays

    Paul Bernays

    Paul_Bernays

  • Algebra of sets
  • Identities and relationships involving sets

    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

    Algebra of sets

    Algebra_of_sets

  • Foundations of mathematics
  • Basic framework of mathematics

    excluded. 1920: Thoralf Skolem corrected Leopold Löwenheim's proof of what is now called the downward Löwenheim–Skolem theorem, leading to Skolem's paradox discussed

    Foundations of mathematics

    Foundations of mathematics

    Foundations_of_mathematics

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THORALF SKOLEM

  • Thorlak
  • Boy/Male

    Norse

    Thorlak

    Bishop of Skalholt.

    Thorlak

  • Thoralf
  • Boy/Male

    Danish, German, Norwegian, Swedish

    Thoralf

    God of Thunder

    Thoralf

  • Thornly
  • Boy/Male

    American, British, English

    Thornly

    From the Thorny Meadow

    Thornly

  • Thorvald
  • Boy/Male

    Norse

    Thorvald

    Son of Asvald.

    Thorvald

  • Thorold
  • Boy/Male

    British, English, Norse

    Thorold

    Follower of Thor

    Thorold

  • Thrall
  • Surname or Lastname

    English

    Thrall

    English : status name from Old English þrǣl ‘thrall’, ‘serf’ (from Old Norse þræll).

    Thrall

  • Thoraya |
  • Girl/Female

    Muslim

    Thoraya |

    Star

    Thoraya |

  • THORA
  • Female

    Scandinavian

    THORA

    Variant spelling of Scandinavian Tora, THORA means "Thor" or "thunder."

    THORA

  • Vestar
  • Boy/Male

    Norse

    Vestar

    Son of Thorolf.

    Vestar

  • Thoraya
  • Girl/Female

    Muslim/Islamic

    Thoraya

    Star

    Thoraya

  • Galm
  • Boy/Male

    Norse

    Galm

    Father of Thorvald.

    Galm

  • THORVALD
  • Male

    Swedish

    THORVALD

    Danish and Swedish form of Old Norse Þorvaldr, THORVALD means "Thor's ruler." 

    THORVALD

  • Thrasi
  • Boy/Male

    Norse

    Thrasi

    Son of Thorolf.

    Thrasi

  • Thorald
  • Boy/Male

    Australian, Danish, Dutch, German, Norse

    Thorald

    Thor Ruler; Follower of Thor

    Thorald

  • Thorolf
  • Boy/Male

    Norse

    Thorolf

    Thor's wolf.

    Thorolf

  • Thoraya
  • Girl/Female

    Arabic, Muslim

    Thoraya

    Star

    Thoraya

  • Thorvald
  • Boy/Male

    Danish, German, Norse, Norwegian, Swedish

    Thorvald

    Thunder; Son of Asvald

    Thorvald

  • Toralf
  • Boy/Male

    Danish, French, German, Swedish

    Toralf

    God of Thunder

    Toralf

  • Thorald
  • Boy/Male

    Norse

    Thorald

    Thor ruler.

    Thorald

  • Thir
  • Girl/Female

    Norse

    Thir

    Wife of Thrall.

    Thir

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THORALF SKOLEM

  • Thrall
  • n.

    A slave; a bondman.

  • Choristic
  • a.

    Choric; choral.

  • Horaly
  • adv.

    Hourly.

  • Choral
  • a.

    Of or pertaining to a choir or chorus; singing, sung, or adapted to be sung, in chorus or harmony.

  • Thrall
  • n.

    Slavery; bondage; servitude; thraldom.

  • Thrall-like
  • a.

    Resembling a thrall, or his condition, feelings, or the like; slavish.

  • Thorax
  • n.

    The second, or middle, region of the body of a crustacean, arachnid, or other articulate animal. In the case of decapod Crustacea, some writers include under the term thorax only the three segments bearing the maxillipeds; others include also the five segments bearing the legs. See Illust. in Appendix.

  • Intrathoracic
  • a.

    Within the thora/ or chest.

  • Thrall
  • n.

    A shelf; a stand for barrels, etc.

  • Corselet
  • n.

    The thorax of an insect.

  • Thrall
  • a.

    Of or pertaining to a thrall; in the condition of a thrall; bond; enslaved.

  • Thorax
  • n.

    The part of the trunk between the neck and the abdomen, containing that part of the body cavity the walls of which are supported by the dorsal vertebrae, the ribs, and the sternum, and which the heart and lungs are situated; the chest.

  • Thoral
  • a.

    Of or pertaining to a bed.

  • Thrall
  • v. t.

    To enslave.

  • Choralist
  • n.

    A singer or composer of chorals.

  • Choral
  • n.

    A hymn tune; a simple sacred tune, sung in unison by the congregation; as, the Lutheran chorals.

  • Baenosome
  • n.

    The thorax of Arthropods.

  • Thorax
  • n.

    A breastplate, cuirass, or corselet; especially, the breastplate worn by the ancient Greeks.

  • Interthoracic
  • a.

    In the thorax.

  • Thorax
  • n.

    The middle region of the body of an insect, or that region which bears the legs and wings. It is composed of three united somites, each of which is composed of several distinct parts. See Illust. in Appendix. and Illust. of Coleoptera.