axiom rank
1Rank-into-rank — In set theory, a branch of mathematics, a rank into rank is a large cardinal lambda; satisfying one of the following four axioms (commonly known as rank into rank embeddings, given in order of increasing consistency strength):*Axiom I3: There is… …
2Axiom schema of replacement — In set theory, the axiom schema of replacement is a schema of axioms in Zermelo Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite… …
3Axiom of global choice — In class theories, the axiom of global choice is a stronger variant of the axiom of choice which applies to proper classes as well as sets. Statement The axiom can be expressed in various ways which are equivalent: Weak form: Every class of… …
4Independence of irrelevant alternatives — (IIA) is an axiom of decision theory and various social sciences. The word is used in different meanings in different contexts. Although they all attempt to provide a rational account of individual behavior or aggregation of individual… …
5Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects …
6New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …
7Implementation 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… …
8List of axioms — This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self evidence. Individual axioms are almost always part of a larger axiomatic… …
9List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …
10Von Neumann universe — In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is… …
