Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

In set theory, the complement of a set A, often denoted by A c {\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the...

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations...

Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

Appendix:Glossary of set theory in Wiktionary, the free dictionary. This is a glossary of terms and definitions related to the topic of set theory. Contents: ...

example being the neighborhood filter. Filters appear in order theory, model theory, and set theory, but can also be found in topology, from which they originate...

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...

graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set S...

In set theory, a tree is a partially ordered set ( T , < ) {\displaystyle (T,<)} such that for each t ∈ T {\displaystyle t\in T} , the set { s ∈ T : s...

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts...

Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness...

Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces...

Look up set theory in Wiktionary, the free dictionary. Set theory is a branch of mathematics concerning mathematical sets. A set theory may also refer...

In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by c {\displaystyle...

Internal set theory Pocket set theory Naive set theory S (set theory) Double extension set theory Kripke–Platek set theory Kripke–Platek set theory with urelements...

conditions for a topological space to be metrizable. Set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological...

"Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University Suppes, Patrick (1972) [1960], Axiomatic Set Theory,...

In mathematical set theory, the multiverse view is that there are many models of set theory, but no "absolute", "canonical" or "true" model. The various...

In descriptive set theory, a tree on a set X {\displaystyle X} is a collection of finite sequences of elements of X {\displaystyle X} such that every...

in set theory, the constructible universe (or Gödel's constructible universe), denoted by L , {\displaystyle L,} is a particular class of sets that...

Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and analysis of discrete mathematics to properties...

In set theory, the kernel of a function f {\displaystyle f} (or equivalence kernel) may be taken to be either the equivalence relation on the function's...

In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary...

Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic...

specific set of other sentences. The sentences in this set are referred to as "axioms". A sentence σ is independent of a given first-order theory T if T...

In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension holds for at least the...