finite von Neumann ordinal

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• Von 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… …   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

• von Neumann, John — orig. Johann Von Neumann born Dec. 3, 1903, Budapest, Hung. died Feb. 8, 1957, Washington, D.C., U.S. Hungarian born U.S. mathematician. After receiving his Ph.D. from the University of Budapest, he emigrated to the U.S. to teach at Princeton… …   Universalium

• Von Neumann cardinal assignment — The von Neumann cardinal assignment is a cardinal assignment which uses ordinal numbers. For a well ordered set U , we define its cardinal number to be the smallest ordinal number equinumerous to U . More precisely,:|U| = mathrm{card}(U) = inf {… …   Wikipedia

• John von Neumann — Von Neumann redirects here. For other uses, see Von Neumann (disambiguation). The native form of this personal name is Neumann János. This article uses the Western name order. John von Neumann …   Wikipedia

• Ordinal number — This article is about the mathematical concept. For number words denoting a position in a sequence ( first , second , third , etc.), see Ordinal number (linguistics). Representation of the ordinal numbers up to ωω. Each turn of the spiral… …   Wikipedia

• Finite 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… …   Wikipedia

• Ordinal definable set — In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first order formula. Ordinal definable sets were introduced by Gödel (1965). A drawback to this… …   Wikipedia

• Limit ordinal — A limit ordinal is an ordinal number which is neither zero nor a successor ordinal. Various equivalent ways to express this are: *It cannot be reached via the ordinal successor operation S ; in precise terms, we say lambda; is a limit ordinal if… …   Wikipedia

• Universe (mathematics) — In mathematical logic, the universe of a structure (or model ) is its domain.In mathematics, and particularly in applications to set theory and the foundations of mathematics, a universe or universal class (or if a set, universal set – not to be… …   Wikipedia

• Natural number — Natural numbers can be used for counting (one apple, two apples, three apples, ...) from top to bottom. In mathematics, the natural numbers are the ordinary whole numbers used for counting ( there are 6 coins on the table ) and ordering ( this is …   Wikipedia