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Quantified formulas with real-number variables
computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form ∃ X 1 ⋯ ∃ X n F (
Existential theory of the reals
Existential_theory_of_the_reals
Geometric graph with unit edge lengths
specifically complete for the existential theory of the reals. The unit distance graph for a set of points in the plane is the undirected graph having those
Unit_distance_graph
Field in mathematics similar to the real numbers
The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals". Journal of Symbolic Computation. 13 (3): 255–299
Real_closed_field
Method for solving one problem using another
well. An example of this is the complexity class ∃ R {\displaystyle \exists \mathbb {R} } defined from the existential theory of the reals, a computational
Polynomial-time_reduction
American mathematician
deciding the existential theory of the reals" (PDF). Technical Report No. 792. School of Operations Research and Industrial Engineering, College of Engineering
James_Renegar
Topics referred to by the same term
symbol Etravirine, a drug used to suppress HIV replication Existential theory of the reals, formal language in computer science Express Toll Route, in
ETR
Fewest edge crossings in drawing of a graph
removal of a single edge). A closely related problem, determining the rectilinear crossing number, is complete for the existential theory of the reals. On
Crossing number (graph theory)
Crossing_number_(graph_theory)
Three-dimensional Ising model Existential theory of the reals § Complete problems Karp's 21 NP-complete problems List of PSPACE-complete problems Reduction
List_of_NP-complete_problems
Subset of n-space defined by a finite sequence of polynomial equations and inequalities
lies inside an algebraic subvariety of the same dimension. Łojasiewicz inequality Existential theory of the reals Subanalytic set Piecewise algebraic
Semialgebraic_set
Philosophy dealing with absurdity of existence
incomprehensibility of existence. In examining meaning, purpose, and value, existentialist thought often includes concepts such as existential crises, angst
Existentialism
Geometric concept
1\}\right\}.} Thus the problem for each dimension can be expressed in the existential theory of the reals. However, general methods of solving problems
Kissing_number
Mathematical use of "there exists"
an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually denoted by the logical
Existential_quantification
Form of psychotherapy
Existential therapy is a form of psychotherapy focused on the client's lived experience of their subjective reality. The aim is for clients to use their
Existential_therapy
Graph representing intersections between given sets
complete for the existential theory of the reals (Schaefer 2010). The line graph of a graph G is defined as the intersection graph of the edges of G, where
Intersection_graph
first-order language of the real numbers is the set of all well-formed sentences of first-order logic that involve universal and existential quantifiers and
Decidability of first-order theories of the real numbers
Decidability_of_first-order_theories_of_the_real_numbers
Unsolved problem in combinatorial geometry
each one while maintaining the order in which each crosses each other, but it is complete for the existential theory of the reals to distinguish stretchable
Kobon_triangle_problem
Theory that life has no inherent meaning
Existential nihilism is the philosophical theory that life has no objective meaning or purpose. The inherent meaninglessness of life is largely explored
Existential_nihilism
Combinitorics of Polyhedra
of simplicial polytopes, which was shown to be complete for the existential theory of the reals by Adiprasito & Padrol (2017). In the context of the simplex
Polyhedral_combinatorics
Graph of intervisible locations in computational geometry
Euclidean plane is complete for the existential theory of the reals. The art gallery problem is the problem of finding a small set of points such that all other
Visibility_graph
Integer associated with a graph
for the existential theory of the reals, to test whether the dimension or the Euclidean dimension of a given graph is at most a given value. The problem
Dimension_(graph_theory)
Graph-theoretic description of polyhedra
existential theory of the reals, even for four-dimensional polytopes, by Richter-Gebert's universality theorem. Here, the existential theory of the reals
Steinitz's_theorem
Intersection graph of unit disks in the plane
exponentially as a function of the dimension. It is NP-hard (more specifically, complete for the existential theory of the reals) to determine whether a graph
Unit_disk_graph
Problems which attempt to find the most efficient way to pack objects into containers
of deciding whether a given set of polygons can fit in a given square container has been shown to be complete for the existential theory of the reals
Packing_problems
Psychological perspective
Among the earliest approaches we find the developmental theory of Abraham Maslow, emphasizing a hierarchy of needs and motivations; the existential psychology
Humanistic_psychology
Graph with edges of length one, able to be drawn without crossings
matchstick graph. More precisely, this problem is complete for the existential theory of the reals. Kurz (2011) provides some easily tested necessary criteria
Matchstick_graph
Hypothesized risk to human existence
cause an existential catastrophe. In 2023, hundreds of AI experts and other notable figures signed a statement declaring, "Mitigating the risk of extinction
Existential risk from artificial intelligence
Existential_risk_from_artificial_intelligence
Anxiety caused by thoughts of death
management theory, as well as in similar theories, is the increase in existential death anxiety that people experience. Existential death anxiety is the belief
Death_anxiety
Minimum-cost tree with exactly k vertices
in the class of problems reducible to the existential theory of the reals. The k-minimum spanning tree may be found in polynomial time for graphs of bounded
K-minimum_spanning_tree
Rejection of certain ideas about reality
Forms of nihilism belonging to the fields of ethics and value theory question the existence of values, morality, and the meaning of life. Existential nihilism
Nihilism
Australian computer scientist
seminal contributions in the areas of robotics and machine perception. Canny edge detector Existential theory of the reals Kinodynamic planning Canny
John_Canny
Assignment of colors to edges of a graph
complete for the existential theory of the reals, a complexity class at least as difficult as being NP-complete. As well as being related to the maximum degree
Edge_coloring
Pseudolines arranged largely to study arrangements of lines
stretchability is a difficult computational task: it is complete for the existential theory of the reals to distinguish stretchable arrangements from non-stretchable
Arrangement_of_pseudolines
Number of edge slopes in graph drawing
with slope number two, and hard for the existential theory of the reals to determine the minimum slope number of a planar drawing. Proved independently
Slope_number
model theory, a branch of mathematical logic, the notion of an existentially closed model (or existentially complete model) of a theory generalizes the notions
Existentially_closed_model
Irrational system of points and lines
visibility graphs of finite point sets is hard for the existential theory of the reals, Cardinal and Hoffman in 2017 showed how to convert problems of testing whether
Perles_configuration
Axiomatic set theories based on the principles of mathematical constructivism
separation prove the collection of Cauchy reals to be a set, thus somewhat simplifying the logically treatment of the reals. Even in the strong theory I Z F {\displaystyle
Constructive_set_theory
Mathematical use of "for all" and "there exists"
quantifications or existential quantifications) can be exchanged without changing the meaning of the statement. In contrast, the exchange of quantifications
Quantifier_(logic)
Form of logic that allows quantification over predicates
isomorphic to the real number field. On the other hand, the set of first-order sentences valid in the reals has arbitrarily large models due to the compactness
Second-order_logic
First article on transfinite set theory
published proof and the reverse-order proof both use the theorem: Given a sequence of reals, a real can be found that is not in the sequence. By applying
Cantor's first set theory article
Cantor's_first_set_theory_article
Social and evolutionary psychology theory
management theory (TMT) is a theory in social and evolutionary psychology which proposes a basic psychological conflict stemming from two competing facts of human
Terror_management_theory
Graph theory representation
existential theory of the reals. The RAC drawing problem remains NP-hard for upward drawing of directed acyclic graphs. However, in the special case of outer-1-planar
RAC_drawing
Conspiracy theory about race and culture
conspiracy theory coined by French author Renaud Camus. Camus's theory states that, with the complicity or cooperation of "replacist" elites, the ethnic French
Great Replacement conspiracy theory
Great_Replacement_conspiracy_theory
Mathematical analysis
locatedness of the reals. The theory shall validate further axioms concerning the relation between the positivity predicate x > 0 {\displaystyle x>0} and the algebraic
Constructive_analysis
Type whose definition depends on a value
depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's
Dependent_type
precisely, it is complete for the existential theory of the reals. The proof of this result also implies that for some pairs of graphs that have simultaneous
Simultaneous_embedding
Subdivision of the plane by lines
complete for the existential theory of the reals to distinguish stretchable arrangements from non-stretchable ones. Every arrangement of finitely many
Arrangement_of_lines
Concept in model theory
ℵ0-Categorical Theories". Proceedings of the American Mathematical Society. 39 (3): 591–598. Simmons, H. (1976). "Large and Small Existentially Closed Structures"
Model_complete_theory
Model of computation over real numbers
over reals in a single time step. It is closely related to the real RAM model. BSS machines are more powerful than Turing machines, because the latter
Blum–Shub–Smale_machine
Pollack, Richard; Marie-Francoise, Roy (2003). "Existential Theory of the Reals". Algorithms in Real Algebraic Geometry. Algorithms and Computation in
Graph_flattenability
Summary of a mathematical proof
article gives a sketch of a proof of the first of Gödel's incompleteness theorems. This theorem applies to any formal theory that satisfies certain technical
Proof sketch for Gödel's first incompleteness theorem
Proof_sketch_for_Gödel's_first_incompleteness_theorem
Attributing events to an improbable conspiracy
A conspiracy theory is an explanation for an event or situation that asserts the existence of a conspiracy (generally by powerful sinister groups, often
Conspiracy_theory
American psychologist (1909–1994)
May (April 21, 1909 – October 22, 1994) was an American existential psychologist and author of the influential book Love and Will (1969). He is often associated
Rollo_May
Eight-stage model of psychoanalytic development
that theory wouldn't be able to explain their experiences alone. Existential Question: Can I Trust the World? The first stage of Erik Erikson's theory centers
Erikson's stages of psychosocial development
Erikson's_stages_of_psychosocial_development
Statement that is taken to be true
metatheorems of our theory of mathematical logic since we are dealing with the very concept of proof itself. Aside from this, we can also have existential generalization:
Axiom
State of being real
existence is not a real predicate. Brentano used this idea to develop his theory of judgments, which states all judgments are existential judgments; they
Existence
Austrian neurologist (1905–1997)
school of psychotherapy that describes a search for a life's meaning as the central human motivational force. Logotherapy is part of existential and humanistic
Viktor_Frankl
End of the human species
consequences of overexploitation. Toby Ord's 2020 book The Precipice argues that preventing existential risks is one of the most important moral issues of our
Human_extinction
Hypothetical global-scale disaster risk
potential. In the 21st century, a number of academic and non-profit organizations have been established to research global catastrophic and existential risks
Global_catastrophic_risk
semantics, is a good match. On the other hand Brouwer's long efforts on 'species', as he called the intuitionistic theory of reals, are presumably in some way
History_of_topos_theory
Famous existential psychology case study
his existence." In the arena of existential psychology, Binswanger concluded that her bulimia was the expression of an existential vacuum to fill up her
Ellen_West
Algebraic structure with addition, multiplication, and division
characterization of the reals. The hyperreals R* form an ordered field that is not Archimedean. It is an extension of the reals obtained by including infinite
Field_(mathematics)
Sense or significance of an entity
Groothuis 2020, pp. 162–164 Seachris, § 3. Theories of Meaning in Life Metz 2023, 4. Nihilism Pratt, § 3. Existential Nihilism Crosby 1988, pp. 30–32 Nöth 1990
Meaning_(philosophy)
Theory of personality development
The theory of positive disintegration (TPD) is a theory of personality development developed by Polish psychologist Kazimierz Dąbrowski. Unlike mainstream
Positive_disintegration
Philosophical concept of emptiness
states, and the nature of reality itself. In literature, the Void often serves as a metaphor for existential despair, the search for meaning, or the confrontation
The_Void_(philosophy)
Mathematical system
is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation
Second-order_arithmetic
Alternative foundation of mathematics
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of mathematics
Intuitionistic_type_theory
Unorthodox Scottish psychiatrist (1927–1989)
views on the causes and treatment of psychopathological phenomena were influenced by his study of existential philosophy and ran counter to the chemical
R._D._Laing
English existential risk research centre
The Centre for the Study of Existential Risk (CSER) is a research centre at the University of Cambridge, intended to study possible extinction-level threats
Centre for the Study of Existential Risk
Centre_for_the_Study_of_Existential_Risk
Complexity class used to classify decision problems
EXPSPACE}}} . In terms of descriptive complexity theory, NP corresponds precisely to the set of languages definable by existential second-order logic (Fagin's
NP_(complexity)
Form of logic
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free
Free_logic
Type of AI with wide-ranging abilities
over whether AGI represents an existential risk. Some AI experts and industry figures have stated that mitigating the risk of human extinction posed by AGI
Artificial general intelligence
Artificial_general_intelligence
Set with operations obeying given axioms
shows that existential axioms of the above form are accepted in the definition of a variety. Here are some of the most common existential axioms. Identity
Algebraic_structure
Attempt to persuade or to determine the truth of a conclusion
may or may not be rich, in consideration of the premises as such. (See also: Existential import). The forms of argument that render deductions valid are
Argument
Area of mathematical logic
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing
Model_theory
Feminist movement
greatly to existential feminism through works like Existential Psychoanalysis. In this work, Sartre claims that the individual is the intersection of universal
Feminist_existentialism
Hypothesis about intelligent agents
program them to eliminate existential risk to human beings' safety. The paperclip maximizer example illustrates the broad problem of managing powerful systems
Instrumental_convergence
Far-right antisemitic conspiracy theory
Marxism is a far-right and antisemitic conspiracy theory that misrepresents Western Marxism (especially the Frankfurt School) as being responsible for modern
Cultural Marxism conspiracy theory
Cultural_Marxism_conspiracy_theory
Branch of logic
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax)
Finite_model_theory
Object(s) postulated to exist by a given language
phrase of 'existential quantification', like 'There are some so-and-sos', then one must either (1) admit that one is committed to the existence of things
Ontological_commitment
Philosphical view that existence proofs must be constructive
constructivist might reject it. The constructive viewpoint involves a verificational interpretation of the existential quantifier, which is at odds with
Constructivism (philosophy of mathematics)
Constructivism_(philosophy_of_mathematics)
British philosopher, author (born 1964)
others. The book stresses the importance of individuality, unique character and personal, existential freedom and is critical of what it sees as the devisive
Gary_Cox_(philosopher)
Type of uncertainty of meaning where several interpretations are possible
of signification. Thus, although some things may be certain, they have little to do with Dasein's sense of care and existential anxiety, e.g., in the
Ambiguity
Whether a decision problem has an effective method to derive the answer
the theory of real closed fields, and Presburger arithmetic, while the theory of groups and Robinson arithmetic are examples of undecidable theories. Some
Decidability_(logic)
Recognition of an employee by a supervisor
Herzberg 1966; Maslow 1943) theories and reinforcement theory (Mainly Pavlov 1902; B.F. Skinner 1938) as a foundation for the effects of employee recognition
Employee_recognition
Standard system of axiomatic set theory
formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice
Zermelo–Fraenkel_set_theory
Mathematical construction
subset of the hyperreals, and they have the same first-order properties as the rationals. Consider, however, the Archimedean property of the reals, which
Ultraproduct
American conspiracy theory and political movement
American political conspiracy theory and political movement that originated in 2017. QAnon centers on the fabrications of an anonymous individual or individuals
QAnon
Major unsolved problem in transcendental number theory
transcendental number theory, Schanuel's conjecture is a conjecture about the transcendence degree of certain field extensions of the rational numbers Q
Schanuel's_conjecture
3-volume treatise on mathematics, 1910–1913
only set theory, cardinal numbers, ordinal numbers, and real numbers. Deeper theorems from real analysis were not included, but by the end of the third volume
Principia_Mathematica
Philosophical category of inexpressible reality
expression. The Real is the intelligible form of the horizon of truth of the field-of-objects that has been disclosed. As the Real Order of the Borromean
The_Real
Mathematical use of "for all"
distinct from existential quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. Quantification
Universal_quantification
Form of psychotherapy
therapy and the transference-oriented approaches; between the existential, phenomenological, and hermeneutical aspects of gestalt therapy and the constructivist
Gestalt_therapy
Allegory by Plato
"Discovering the unhidden: Heidegger's Interpretation of Plato's Allegory of the Cave and its Implications for Psychotherapy". Existential Analysis. 22
Allegory_of_the_cave
American scientist (1839–1914)
major contributions to logic, such as theories of relations and quantification. C. I. Lewis wrote, "The contributions of C. S. Peirce to symbolic logic are
Charles_Sanders_Peirce
Concept in existential psychology and philosophy
Authenticity is a concept of personality in the fields of psychology, existential psychotherapy, existentialist philosophy, and aesthetics. In existentialism
Authenticity_(philosophy)
Set of therapeutic techniques established by Sigmund Freud
treating mental disorders. Established in the early 1890s by Sigmund Freud, it takes into account Darwin's theory of evolution, neurology findings, ethnology
Psychoanalysis
Hungarian-American family therapist
psychological, interpersonal, existential, systemic, and intergenerational dimensions of individual and family life and development. The contextual model, in its
Ivan_Boszormenyi-Nagy
Mathematical theory of data types
In mathematical logic, and theoretical computer science, type theory is the study of formal systems that classify expressions or mathematical objects by
Type_theory
Concept in the philosophy of science
observable. ... There were certain [existential] conditions postulated in the content of the new [non-existential] conception about dew, and it had to
Natural_kind
The white genocide, white extinction, or white replacement conspiracy theory is a white nationalist conspiracy theory that claims there is a deliberate
White genocide conspiracy theory
White_genocide_conspiracy_theory
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