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Subfield of set theory
Determinacy is a subfield of game theory and set theory that examines the conditions under which one or the other player of a game has a winning strategy
Determinacy
Possible axiom for set theory
In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962
Axiom_of_determinacy
projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy, abbreviated
Projective_determinacy
Theorem in descriptive set theory
In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that
Borel_determinacy_theorem
Kinematic determinacy is a term used in structural mechanics to describe a structure where material compatibility conditions alone can be used to calculate
Kinematic_determinacy
Abstract strategy board game
published a proof that the determinacy of Hex is equivalent to the two-dimensional Brouwer fixed-point theorem, and that the determinacy of higher-dimensional
Hex_(board_game)
Branch of mathematics that studies sets
is common in the study of determinacy and large cardinals, especially when considering axioms such as the axiom of determinacy that contradict the axiom
Set_theory
Philosophical terms
article on a computer. But in an examination of the possibility of the determinacy of any possible concept, differences like this are supremely relevant
Indeterminacy_(philosophy)
American mathematician (born 1955)
has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, bears his name. In
W._Hugh_Woodin
real determinacy Von Neumann–Bernays–Gödel axioms Continuum hypothesis and its generalization Freiling's axiom of symmetry Axiom of determinacy Axiom
List_of_axioms
American mathematician (born 1948)
contributions to the theory of inner models and determinacy. With Donald A. Martin, he proved projective determinacy, assuming the existence of sufficiently large
John_R._Steel
When a structure's static equilibrium equations have no unique solution
necessary for stability. Christian Otto Mohr Flexibility method Kinematic determinacy Overconstrained mechanism Structural engineering Matheson, James Adam
Statically_indeterminate
Axiom of set theory
In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following: Axiom—Consider infinite two-person
Axiom_of_real_determinacy
Facts provided or learned about something or someone
Information is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation
Information
Structural engineering theory is the application of physics and mathematics to analyze and design structures to ensure they can withstand loads. Structural
Structural_engineering_theory
Theory of equilibrium between supply and demand
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting
General_equilibrium_theory
Mathematical system
projective determinacy are hard to find. ZFC + {there are n Woodin cardinals: n is a natural number} is conservative over Z2 with projective determinacy[citation
Second-order_arithmetic
analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. That is, if a measure μ {\displaystyle \mu } satisfies
Carleman's_condition
Infinite game in descriptive set theory whose payoff set is a lightface analytic set
payoff set is a lightface analytic (Σ11) subset of Baire space. The determinacy of all lightface analytic games is equivalent, over ZFC, to the existence
Lightface_analytic_game
Universally measurable set Determinacy AD+ Axiom of determinacy Axiom of projective determinacy Axiom of real determinacy Empty set Forcing (mathematics)
List_of_set_theory_topics
Branch of mathematical logic
recursion, ∆0 2 determinacy, and the ∆1 1 Ramsey theorem are all equivalent to each other. Over RCA0, Σ1 1 monotonic induction, Σ0 2 determinacy, and the Σ1
Reverse_mathematics
Broadest definition of sizes in integer-dimensional spaces
Lebesgue measure 0. If the axiom of determinacy holds then all sets of reals are Lebesgue-measurable. Determinacy is however not compatible with the axiom
Lebesgue_measure
Russian mathematician and sociologist
to sociological analysis. He is best known for creating and defining determinacy analysis and the theory of rules. Sergey Chesnokov was born on 29 June
Sergey_Chesnokov
Topics referred to by the same term
Determined: A Science of Life Without Free Will, 2023 book by Robert Sapolsky Determinacy, a subfield of game theory and set theory This disambiguation page lists
Determined
Trying to map moments to a measure that generates them
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ {\displaystyle \mu } to the sequence of moments
Moment_problem
Infinite Cardinal number
equinumerous with W α ( A ) {\displaystyle W_{\alpha }(A)} .) Borel determinacy is implied by the existence of all beths of countable index. Uncountable
Beth_number
Size of a set in mathematics
multiverse of set theories, but no "absolute" or "true" model. The Axiom of Determinacy (AD) asserts that certain kinds of mathematical games on the natural
Cardinality
Set theory axiom extension
theory, AD+ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy. The axiom, which is to be understood in the context of ZF plus DCR (the
AD+
American mathematician
involved the descriptive set-theoretic consequences of the axiom of determinacy. In particular he is known for having calculated the values of all the
Steve_Jackson_(mathematician)
Deductive system in set theory
theory of determinacy of pointclasses to cover the structure H ℵ 2 {\displaystyle H_{\aleph _{2}}} . Just as the axiom of projective determinacy yields a
Ω-logic
Israeli mathematician
Angeles. He has made major contributions to the theory of inner models, determinacy and forcing. Neeman was born in 1972 in Safed, Israel. After studying
Itay_Neeman
Device which holds a mirror
This type of mount is designed according to the principles of kinematic determinacy. Typically, the movable frame that holds the mirror pivots on a ball
Mirror_mount
Fourth letter in the Greek alphabet
symbol of dentistry. The anonymous signature of James David Forbes. Determinacy (having a definite truth-value) in philosophical logic. In mathematics
Delta_(letter)
Subfield of mathematical logic
Baire. This is related to the fact that ZFC proves Borel determinacy, but not projective determinacy. There are also generic extensions of L {\displaystyle
Descriptive_set_theory
Field of engineering dealing with extremely low tolerances
precision Flexures Kinematic coupling Measurement uncertainty Kinematic determinacy This article incorporates public domain material from the National Institute
Precision_engineering
Finite ordered list of elements
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Tuple
American mathematician (born 1940)
notable works are the proofs of analytic determinacy (from the existence of a measurable cardinal), Borel determinacy (from ZFC alone), the proof (with John
Donald_A._Martin
American mathematician
Paris–Harrington theorem along with Jeff Paris, showing that if the axiom of determinacy holds for all analytic sets then x# exists for all reals x, and proving
Leo_Harrington
Term in mathematical logic
added hypothesis that ZF is consistent. The axiom of determinacy The axiom of real determinacy AD+ A set of sentences is independent, or simply independent
Independence (mathematical logic)
Independence_(mathematical_logic)
Topics referred to by the same term
computer-networking environment) Zermelo–Fraenkel set theory with the axiom of determinacy This disambiguation page lists articles associated with the title ZFD
ZFD
Concept in set theory
the existence of 0 ♯ {\displaystyle 0^{\sharp }} is equivalent to the determinacy of lightface analytic games. In fact, the strategy for a universal lightface
Zero_sharp
Existence of 0# Singular cardinals hypothesis Projective determinacy (and even the full axiom of determinacy if the axiom of choice is not assumed) There are
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Concept in mathematical logic
connection with strong partition cardinals and the axiom of determinacy. The axiom of determinacy is equivalent to the existence of unboundedly many strong
Theta_(set_theory)
Mathematical game played on a directed graph
for n = 2), where determinacy of such games was proven. The Knaster–Tarski theorem leads to a relatively simple proof of determinacy of parity games. Moreover
Parity_game
industry. These requirements are, in no particular order: Robustness, Determinacy, Compatibility. Robustness includes requirements such as connection redundancy
Process_control_network
Axiom of set theory
that are not compatible with the axiom of choice, such as the axiom of determinacy. While some varieties of constructive mathematics avoid the axiom of
Axiom_of_choice
Clade of seed plants that produce flowers
ISBN 978-1-4398-4436-6. Bortiri, E.; Hake, S. (13 January 2007). "Flowering and determinacy in maize". Journal of Experimental Botany. 58 (5). Oxford University
Flowering_plant
Type of perfect Bayesian equilibrium
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Separating_equilibrium
Topics referred to by the same term
dead reckoning, GNSS-assisted dead reckoning for vehicles Axiom of real determinacy Azerbaijan Democratic Republic (1918–1920), a precursor state to modern
ADR
Israeli mathematician and computer scientist (1931–2026)
n = 2) is decidable. A key component of the proof implicitly showed determinacy of parity games, which lie in the third level of the Borel hierarchy
Michael_O._Rabin
German mathematician and logician
Berkeley. In 2001, he completed his PhD entitled Blackwell Determinacy about determinacy under supervision of Donald A. Martin and Ronald Björn Jensen
Benedikt_Löwe
Difference of an open set by a meager set
\Gamma } has the property of Baire. Therefore, it follows from projective determinacy, which in turn follows from sufficient large cardinals, that every projective
Property_of_Baire
sets, Σ1n sets, or Π1n sets. It follows from determinacy of differences of sets in Γ. Since Borel determinacy is proved in ZFC, ZFC implies Wadge's lemma
Wadge_hierarchy
Mathematical models of strategic interactions
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Game_theory
Topics referred to by the same term
Photodynamic Therapy Point-defence, a category of weapons Axiom of projective determinacy, in mathematical logic Pumpe Düse, a Volkswagen Group name for Unit Injector
PD
Opposite position of realism
the same effect can be produced by multiple causes, there is a lack of determinacy about what one is really perceiving, as in the brain in a vat scenario
Anti-realism
Hand game for two players or more
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Rock_paper_scissors
Plant which completes its life cycle within one growing season and then dies
Rohde, A; Beeckman, T (2008). "Flowering-time genes modulate meristem determinacy and growth form in Arabidopsis thaliana". Nature Genetics. 40 (12): 1489–92
Annual_plant
Generalization of "n-th" to infinite cases
theory without the Axiom of Choice, such as those satisfying the Axiom of determinacy, the club filter on ω 1 {\displaystyle \omega _{1}} can be an ultrafilter
Ordinal_number
French mathematician (1871–1956)
Borel–Cantelli lemma Borel–Carathéodory theorem Heine–Borel theorem Borel determinacy theorem Borel right process Borel set Borel summation Borel distribution
Émile_Borel
Topics referred to by the same term
Determinism theory of hematopoiesis Superdeterminism Deterministic system Determinacy in set theory and game theory Deterministic algorithm Deterministic automaton
Determinism_(disambiguation)
Universally measurable set Determinacy AD+ Axiom of determinacy Axiom of projective determinacy Axiom of real determinacy Empty set Forcing (mathematics)
List of mathematical logic topics
List_of_mathematical_logic_topics
Paper-and-pencil game for two players
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Tic-tac-toe
Varying physical quantity that conveys information
classified into analog signals and digital signals; according to the determinacy of signals, classified into deterministic signals and random signals;
Signal
Search algorithm
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Alpha–beta_pruning
Overuse of a shared resource
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Tragedy_of_the_commons
1994 mathematics book
Woodin cardinals. The book concludes with the chapter "Determinacy", involving the axiom of determinacy and the theory of infinite games. Reviewer Frank R
The_Higher_Infinite
Natural philosophy holding that the world comprises fundamental indivisible components
be considered a composite of form and matter, as it has identity and determinacy to a certain extent, pure or primary matter is completely unformed, unintelligible
Atomism
Proposition in mathematical logic
the axiom of choice (AC) (and therefore the negation of the axiom of determinacy, AD), so choice and GCH are not independent in ZF; there are no models
Continuum_hypothesis
American economist and Nobel Laureate (born 1943)
monetary-policy instruments and rules on output stability and price determinacy. help make the theory of rational expectations statistically operational
Thomas_J._Sargent
Israeli-American psychologist and economist (1934–2024)
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Daniel_Kahneman
Concept in game theory involving long-term strategic planning
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Farsightedness_(game_theory)
Italian economist (born 1961)
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Pierpaolo_Battigalli
Hungarian and American mathematician and physicist (1903–1957)
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
John_von_Neumann
Concept in game theory
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Focal_point_(game_theory)
Mathematical concept
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Equivalence_class
the projective sets and below the sets in L(R). Assuming sufficient determinacy, the class of inductive sets has the scale property and thus the prewellordering
Inductive_set
Smallest transitive inner model of ZF containing all the ordinals and all the reals
L(R) does not satisfy the axiom of choice, but rather the axiom of determinacy. However, L(R) will still satisfy the axiom of dependent choice, given
L(R)
Pair of logical equivalences
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
De_Morgan's_laws
Topics referred to by the same term
representation of a Lie group, abbreviated "Ad" in mathematics Axiom of determinacy, a set theory axiom Antiproton Decelerator, a device at the CERN physics
AD_(disambiguation)
of natural numbers, named after Donald A. Martin. Under the axiom of determinacy it can be shown to be an ultrafilter. Let D {\displaystyle D} be the
Martin_measure
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Nested_set_collection
Set of elements common to all of some sets
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Intersection_(set_theory)
System in mathematical set theory
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Vague_set
Concept in game theory
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Shapley_value
Set of elements in any of some sets
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Union_(set_theory)
Every analytic set is universally measurable. It follows from projective determinacy, which in turn follows from sufficient large cardinals, that every projective
Universally_measurable_set
Theories in mathematical logic
constructibility (V=L) Proper forcing axiom Analytic determinacy, projective determinacy, Axiom of determinacy Many large cardinal axioms Mathematics portal
List_of_first-order_theories
Logical paradox in decision-making theory
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Paradox_of_tolerance
Paradox in set theory
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Russell's_paradox
Descriptive set theory concept
analysis. Strong set-theoretic principles may be stated in terms of the determinacy of various pointclasses, which in turn implies that sets in those pointclasses
Pointclass
Size of a possibly infinite set
Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set
Cardinal_number
Decision rule used for minimizing the possible loss for a worst-case scenario
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Minimax
Russian philosopher (1804–1860)
he have expressed it. Khomyakov's thought tends to evade ontological determinacy, glistening before us in its play of mother-of-pearl. But this play of
Aleksey_Khomyakov
Biological process of getting older
Beeckman T (December 2008). "Flowering-time genes modulate meristem determinacy and growth form in Arabidopsis thaliana". Nature Genetics. 40 (12): 1489–92
Ageing
German philosopher (1806–1856)
closely related to "Philosophy" than to "Religion", based on their shared determinacy and clarity, and a common ethical root. However, Stirner went beyond
Max_Stirner
Situation where total gains match total losses
Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game
Zero-sum_game
Thesis on the nature of computability
distance of the immediately previously observed configuration. "(D) (Determinacy) The immediately recognizable (sub-)configuration determines uniquely
Church–Turing_thesis
Person involved in directing, instructing and training sportspeople
Names Athletic coach, sports coach Activity sectors Physical education, determinacy Description Fields of employment Schools Related jobs Teacher, sports
Coach_(sport)
Technique of using algorithms to create music
Western counterpoint, for example, can often be reduced to algorithmic determinacy. The term can be used to describe music-generating techniques that run
Algorithmic_composition
DETERMINACY
DETERMINACY
DETERMINACY
DETERMINACY
Boy/Male
English
Alert, vigorous. Modern.
Girl/Female
Afghan, Arabic, Indian, Kannada, Muslim
Praiseworthy; Commendable
Female
English
Latin form of Greek Kharis, CHARIS means "charm, grace, kindness."Â In mythology, this is the singular form of plural Kharites (Charites), a name for the goddesses of charm.
Boy/Male
Tamil
Mithreswar | மீதà¯à®°à¯‡à®¸à¯à®µà®¾à®°Â
Boy/Male
Tamil
White falcon
Boy/Male
Hindu, Indian, Traditional
Of whom Death is Afraid; Long Lived
Girl/Female
Afghan, Arabic, Australian, French, Kurdish, Muslim
Heart; Soul
Boy/Male
Hindu, Indian
Brimming
Boy/Male
Tamil
Abhichandra | அபீசஂதà¯à®°Â
Fearless
Girl/Female
Muslim/Islamic
Light
DETERMINACY
DETERMINACY
DETERMINACY
DETERMINACY
DETERMINACY
n.
Determinateness.