17 relations: Axiom of choice, Axiom of determinacy, Axiom of power set, Axiom schema of replacement, Burali-Forti paradox, Cardinality of the continuum, Class (set theory), Hartogs number, Infimum and supremum, Injective function, Model theory, Ordinal number, Prewellordering, Set theory, Surjective function, Theta, Well-order.
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.
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.
In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.
In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.
In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction.
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum.
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
In mathematics, specifically in axiomatic set theory, a Hartogs number is a particular kind of cardinal number.
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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.
In set theory, a prewellordering is a binary relation \le that is transitive, total, and wellfounded (more precisely, the relation x\le y\land y\nleq x is wellfounded).
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
Theta (uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; θῆτα thē̂ta; Modern: θήτα| thī́ta) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth.
In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.