cofinality

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• Cofinality — Not to be confused with cofiniteness. In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A. This definition of cofinality relies on the axiom… …   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

• Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   Wikipedia

• Stationary set — In mathematics, particularly in set theory and model theory, there are at least three notions of stationary set:Classical notionIf kappa is a cardinal of uncountable cofinality, Csubseteqkappa, and C intersects every club in kappa, then C is… …   Wikipedia

• Ordinal collapsing function — In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger …   Wikipedia

• Singular cardinals hypothesis — In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular cardinal.According to Mitchell (1992), the… …   Wikipedia

• List of forcing notions — In mathematics, forcing is a method of constructing new models M[G] of set theory by adding a generic subset G of a poset P to a model M. The poset P used will determine what statements hold in the new universe (the extension ); to force a… …   Wikipedia

• Mahlo cardinal — In mathematics, a Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by Paul Mahlo (1911, 1912, 1913). As with all large cardinals, none of these varieties of Mahlo cardinals can be proved to… …   Wikipedia

• PCF theory — is the name of a mathematical theory, introduced by Saharon Shelah (1978), that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of power sets of singular cardinals, and has… …   Wikipedia

• Easton's theorem — In set theory, Easton s theorem is a result on the possible cardinal numbers of powersets. W. B. harvtxt|Easton|1970 (extending a result of Robert M. Solovay) showed via forcing that : kappa < operatorname{cf}(2^kappa),and, for kappale lambda,,… …   Wikipedia

• König's theorem (set theory) — For other uses, see König s theorem. In set theory, König s theorem (named after the Hungarian mathematician Gyula König) colloquially states that if the axiom of choice holds, I is a set, mi and ni are cardinal numbers for every i in I , and m i …   Wikipedia