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27 relations: Alexander S. Kechris, Analytical hierarchy, Arithmetical hierarchy, Axiom of determinacy, Baire space (set theory), Borel hierarchy, Closure (mathematics), Cofinality, Computational complexity theory, Countable set, Descriptive set theory, Determinacy, Difference hierarchy, Donald A. Martin, Equivalence class, Even and odd ordinals, Game theory, Θ (set theory), Limit ordinal, Lipschitz continuity, Measurable function, Open set, Pointclass, Preorder, Successor ordinal, Veblen function, Zermelo–Fraenkel set theory.
Alexander S. Kechris
Alexander Sotirios Kechris (Αλέξανδρος Σωτήριος Κεχρής; born March 23, 1946) is a set theorist and logician at California Institute of Technology.
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Analytical hierarchy
In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy.
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Arithmetical hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.
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Axiom of determinacy
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.
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Baire space (set theory)
In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology.
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Borel hierarchy
In mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets.
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Closure (mathematics)
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.
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Cofinality
In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A. This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Descriptive set theory
In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces.
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Determinacy
Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies.
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Difference hierarchy
In set theory, the difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences of sets.
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Donald A. Martin
Donald A. Martin (born December 24, 1940), also known as Tony Martin, is an American set theorist and philosopher of mathematics at UCLA, where he is a member of the faculty of mathematics and philosophy.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Even and odd ordinals
In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers.
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Game theory
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
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Θ (set theory)
In set theory, Θ (pronounced like the letter theta) is the least nonzero ordinal α such that there is no surjection from the reals onto α. If the axiom of choice (AC) holds (or even if the reals can be wellordered), then Θ is simply (2^)^+, the cardinal successor of the cardinality of the continuum.
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Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal.
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Lipschitz continuity
In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.
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Measurable function
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Pointclass
In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space.
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Preorder
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.
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Successor ordinal
In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α.
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Veblen function
In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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Semilinear order, Wadge degree, Wadge game, Wadge lemma, Wadge rank, Wadge reducibility, Wadge reducible, Wadge's game, Wadge's lemma.
References
[1] https://en.wikipedia.org/wiki/Wadge_hierarchy
