well-set
121Implementation of mathematics in set theory — This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine s New… …
122Paradoxes of set theory — This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set …
123Zermelo–Fraenkel set theory — Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC consists of a single primitive ontological notion, that of… …
124Non-well-founded set theory — Non well founded set theories are variants of axiomatic set theory which allow sets to contain themselves and otherwise violate the rule of well foundedness. In non well founded set theories, the foundation axiom of ZFC is replaced by axioms… …
125Scott–Potter set theory — An approach to the foundations of mathematics that is of relatively recent origin, Scott–Potter set theory is a collection of nested axiomatic set theories set out by the philosopher Michael Potter, building on earlier work by the mathematician… …
126Finite set — In mathematics, a set is called finite if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. (The value n = 0 is allowed; that is, the empty set is finite.) An infinite set is a set which is… …
127Morse–Kelley set theory — In the foundation of mathematics, Morse–Kelley set theory (MK) or Kelley–Morse set theory (KM) is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory …
128Dedekind-infinite set — In mathematics, a set A is Dedekind infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. A set is Dedekind finite if it is not Dedekind… …
