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27 relations: AD+, Analytic set, Axiom of choice, Axiom of dependent choice, Axiom of determinacy, Axiom of real determinacy, Binary relation, Borel set, Constructible universe, Elementary equivalence, Forcing (mathematics), Inner model, Large cardinal, Lebesgue measure, Ordinal number, Perfect set property, Projective hierarchy, Property of Baire, Real number, Set theory, Transitive set, Uniformization (set theory), Universally measurable set, Von Neumann universe, Wadge hierarchy, Zermelo–Fraenkel set theory, Zero sharp.
AD+
In set theory, AD+ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy.
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Analytic set
In descriptive set theory, a subset of a Polish space X is an analytic set if it is a continuous image of a Polish space.
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Axiom of dependent choice
In mathematics, the axiom of dependent choice, denoted by \mathsf, is a weak form of the axiom of choice (\mathsf) that is still sufficient to develop most of real analysis.
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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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Axiom of real determinacy
In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.
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Constructible universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets that can be described entirely in terms of simpler sets.
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Elementary equivalence
In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences.
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Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results.
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Inner model
In set theory, a branch of mathematical logic, an inner model for a theory T is a substructure of a model M of a set theory that is both a model for T and contains all the ordinals of M.
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Large cardinal
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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Ordinal number
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
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Perfect set property
In descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset (Kechris 1995, p. 150).
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Projective hierarchy
In the mathematical field of descriptive set theory, a subset A of a Polish space X is projective if it is \boldsymbol^1_n for some positive integer n. Here A is.
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Property of Baire
A subset A of a topological space X has the property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is, if there is an open set U\subseteq X such that A \bigtriangleup U is meager (where \bigtriangleup denotes the symmetric difference).
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Transitive set
In set theory, a set A is called transitive if either of the following equivalent conditions hold.
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Uniformization (set theory)
In set theory, the axiom of uniformization, a weak form of the axiom of choice, states that if R is a subset of X\times Y, where X and Y are Polish spaces, then there is a subset f of R that is a partial function from X to Y, and whose domain (in the sense of the set of all x such that f(x) exists) equals Such a function is called a uniformizing function for R, or a uniformization of R. To see the relationship with the axiom of choice, observe that R can be thought of as associating, to each element of X, a subset of Y. A uniformization of R then picks exactly one element from each such subset, whenever the subset is nonempty.
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Universally measurable set
In mathematics, a subset A of a Polish space X is universally measurable if it is measurable with respect to every complete probability measure on X that measures all Borel subsets of X. In particular, a universally measurable set of reals is necessarily Lebesgue measurable (see #Finiteness condition below).
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Von Neumann universe
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well-founded sets.
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Wadge hierarchy
In descriptive set theory, Wadge degrees are levels of complexity for sets of reals.
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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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Zero sharp
In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe.
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References
[1] https://en.wikipedia.org/wiki/L(R)
