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

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

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered...

larger than sets, such as the class of all sets and the class of all ordinals. Morse–Kelley set theory (MK) allows classes to be defined by formulas whose...

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

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

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...

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...

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...

contradictions within modern axiomatic set theory. Set theory as conceived by Georg Cantor assumes the existence of infinite sets. As this assumption cannot be...

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: ...

In set theory and its applications throughout mathematics, a subclass is a class contained in some other class in the same way that a subset is a set contained...

A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection...

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions...

x)} Df. That is, 1 is the class of singletons. This is definition 52.01 (p. 363 ibid.) Class (set theory) – Collection of sets in mathematics that can be...

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...

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

mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine...

In set theory, universes are often classes that contain (as elements) all sets for which one hopes to prove a particular theorem. These classes can serve...

of set classes, by Forte number. In music theory, a set class (an abbreviation of pitch-class-set class) is an ascending collection of pitch classes, transposed...

set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF)...

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...

Zermelo–Fraenkel set theory (ZF) in that it allows proper classes, that is, objects that are not sets, including a class of all sets. It replaces several...

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...

Kripke–Platek set theory (KP), pronounced /ˈkrɪpki ˈplɑːtɛk/, is an axiomatic set theory developed by Saul Kripke and Richard Platek. The theory can be thought...

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...

set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set...

of axiomatic set theory is to distinguish sets from proper classes, if only because mathematics is grounded in sets, with proper classes relegated to...

In set theory, a projection is one of two closely related types of functions or operations, namely: A set-theoretic operation typified by the j {\displaystyle...