axiom of foundation

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• Axiom of regularity — In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo Fraenkel set theory and was introduced by harvtxt|von Neumann|1925. In first order logic the axiom reads::forall A (exists B (B in A)… …   Wikipedia

• foundation — foun·da·tion n 1: a basis upon which something stands or is supported; specif: a witness s preliminary testimony given to identify or explain evidence being offered at trial and establish its connection to the issue for which it is offered the… …   Law dictionary

• Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… …   Wikipedia

• Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …   Wikipedia

• Axiom 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… …   Wikipedia

• foundation — noun Date: 14th century 1. the act of founding 2. a basis (as a tenet, principle, or axiom) upon which something stands or is supported < the foundations of geometry > < the rumor is without foundation in fact > 3. a. funds given for the… …   New Collegiate Dictionary

• foundation — Synonyms and related words: A, a priori principle, affirmation, alpha, anchorage, appanage, apriorism, arrangement, assertion, assumed position, assumption, axiom, basal, base, baseboard, basement, basic, basic training, basis, bearing wall, bed …   Moby Thesaurus

• axiom — Synonyms and related words: a belief, a priori principle, a priori truth, absolute fact, accepted fact, actual fact, adage, admitted fact, affirmation, ana, analects, aphorism, apothegm, apriorism, article of faith, assertion, assumed position,… …   Moby Thesaurus

• Aczel's anti-foundation axiom — is an axiom set forth by harvtxt|Aczel|1988. It states that every finite graph corresponds to one or more sets. In particular, the graph consisting of a single vertex with a loop corresponds to a set which contains itself. See also * Axiom of… …   Wikipedia

• Zermelo–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… …   Wikipedia

• Alain Badiou — Infobox Philosopher region = French philosophy era = Contemporary philosophy color = #B0C4DE image size = 200px image caption = name = Alain Badiou birth = birth date and age|1937|1|17 Rabat, Morocco death = school tradition = Continental… …   Wikipedia