set of axioms

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• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

• Set 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 …   Wikipedia

• Set-theoretic definition of natural numbers — Several ways have been proposed to define the natural numbers using set theory.The contemporary standardIn standard (ZF) set theory the natural numbersare defined recursively by 0 = {} (the empty set) and n +1 = n ∪ { n }. Then n = {0,1,..., n… …   Wikipedia

• Axioms (album) — Infobox Album | Name = Axioms Type = Album Artist = Impossible Recording Machine Released = September 4, 2001 Recorded = ?? Genre = Experimental ambient pop Length = 67:37 Label = Positron! Producer = Impossible Recording Machine Reviews = Last… …   Wikipedia

• Set (mathematics) — This article gives an introduction to what mathematicians call intuitive or naive set theory; for a more detailed account see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory. The intersection of two sets is… …   Wikipedia

• Peano axioms — In mathematical logic, the Peano axioms, also known as the Dedekind Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used… …   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

• Von Neumann–Bernays–Gödel set theory — In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of the canonical axiomatic set theory ZFC. A statement in the language of ZFC is provable in NBG if and only …   Wikipedia

• Morse–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 …   Wikipedia

• Internal set theory — (IST) is a mathematical theory of sets developed by Edward Nelson which provides an axiomatic basis for a portion of the non standard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, the axioms… …   Wikipedia

• Kripke–Platek set theory — The Kripke–Platek axioms of set theory (KP) (IPAEng|ˈkrɪpki ˈplɑːtɛk) are a system of axioms of axiomatic set theory, developed by Saul Kripke and Richard Platek. The axiom system is written in first order logic; it has an infinite number of… …   Wikipedia