cofinality number
1Cofinality — 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… …
2Ordinal 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… …
3Cardinal number — This article describes cardinal numbers in mathematics. For cardinals in linguistics, see Names of numbers in English. In mathematics, cardinal numbers, or cardinals for short, are generalized numbers used to measure the cardinality (size) of… …
4Aleph number — In the branch of mathematics known as set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph (aleph).The… …
5Real 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… …
6Ordinal 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 …
7Singular 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… …
8List 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… …
9Easton'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,,… …
10Cardinal function — In mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers. Contents 1 Cardinal functions in set theory 2 Cardinal functions in topology 2.1 Basic inequalities …
