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19 relations: Axiom of dependent choice, Axiom of determinacy, Axiom of projective determinacy, Axiom of real determinacy, Continuous function, Determinacy, Discrete space, Image (mathematics), Infinity-Borel set, Θ (set theory), Ordinal number, Product topology, Real number, Set (mathematics), Set theory, Suslin's problem, Topological game, W. Hugh Woodin, Zermelo–Fraenkel set theory.
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 projective determinacy
In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets.
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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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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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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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Discrete space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.
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Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
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Infinity-Borel set
In set theory, a subset of a Polish space X is ∞-Borel if it can be obtained by starting with the open subsets of X, and transfinitely iterating the operations of complementation and wellordered union.
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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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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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Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
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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 (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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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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Suslin's problem
In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.
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Topological game
A topological game is an infinite game of perfect information played between two players on a topological space.
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W. Hugh Woodin
William Hugh Woodin (born April 23, 1955) is an American mathematician and set theorist at Harvard University.
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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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