Set theory

In computability theory Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.

In mathematics, there are two different notions of a ring of sets, both referring to certain families of sets.

In mathematics, a multiset (or bag) is a generalization of the concept of a set that, unlike a set, allows multiple instances of the multiset's elements.

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, a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

In mathematics, a finitary relation has a finite number of "places".

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as The principle is more clearly seen in the case of three sets, which for the sets A, B and C is given by Generalizing the results of these examples gives the principle of inclusion–exclusion.

In mathematics, a lattice is one of the fundamental algebraic structures used in abstract algebra.

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

A tuple is a finite ordered list of elements.

In set theory, Ω-logic is an infinitary logic and deductive system proposed by W.

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.

In mathematics, a Sierpiński set is an uncountable subset of a real vector space whose intersection with every measure-zero set is countable.