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searching for Cofinality 13 found (132 total)

alternate case: cofinality

Mahlo cardinal (2,369 words) [view diff] exact match in snippet view article find links to article

an initial subsequence of the cf(κ)-sequence. Thus its cofinality is less than the cofinality of κ and greater than it at the same time; which is a contradiction

Martin's maximum (422 words) [view diff] exact match in snippet view article find links to article

of some regular cardinal κ ≥ ω2 and every element of S has countable cofinality, then there is an ordinal α < κ such that S ∩ α is stationary in α. In

Worldly cardinal (488 words) [view diff] exact match in snippet view article find links to article

not equivalent; in fact, the smallest worldly cardinal has countable cofinality and therefore is a singular cardinal. The following are in strictly increasing

List of forcing notions (2,652 words) [view diff] exact match in snippet view article find links to article

continuum has size at least κ. Here, there is no restriction. If κ has cofinality ω, the cardinality of the reals ends up bigger than κ. Grigorieff forcing

Basic theorems in algebraic K-theory (580 words) [view diff] exact match in snippet view article find links to article

category of free modules and D is the category of projective modules. Cofinality theorem—Let ( A , v ) {\displaystyle (A,v)} be a Waldhausen category that

Diamond principle (692 words) [view diff] exact match in snippet view article find links to article

follows from 2κ = κ+ for stationary S that do not contain ordinals of cofinality κ. Shelah showed that the diamond principle solves the Whitehead problem

Maryanthe Malliaris (461 words) [view diff] exact match in snippet view article find links to article

MS16. Malliaris, M.; Shelah, S. (2016), "Cofinality spectrum theorems in model theory, set theory, and general topology", Journal of the American Mathematical

Saharon Shelah (1,643 words) [view diff] exact match in snippet view article find links to article

Arrow property". arXiv:math/0112213. Malliaris, M.; Shelah, S. (2016). "Cofinality spectrum theorems in model theory, set theory, and general topology".

Covering lemma (716 words) [view diff] exact match in snippet view article find links to article

cardinals correctly (Weak Covering Property). Moreover, if |κ| > ω1, then cofinality((κ+)K) ≥ |κ|. For core models without overlapping total extenders, the

Felix Hausdorff (7,501 words) [view diff] exact match in snippet view article find links to article

-1}^{\aleph _{\alpha }}.} This formula was, together with a later notion called cofinality introduced by Hausdorff, the basis for all further results for Aleph exponentiation

Stability spectrum (731 words) [view diff] exact match in snippet view article find links to article

case holds for cardinals of the form λ = κω, but not for cardinals λ of cofinality ω (because λ < λcof λ). A complete first-order theory T is called totally

Determinacy (4,120 words) [view diff] exact match in snippet view article find links to article

ordinal definable disjoint stationary subsets of κ made of ordinals of cofinality ω. The consistency strength of the determinacy hypothesis is unknown but

Buchholz psi functions (4,795 words) [view diff] exact match in snippet view article find links to article

fundamental sequence for an ordinal number α {\displaystyle \alpha } with cofinality cof ⁡ ( α ) = β {\displaystyle \operatorname {cof} (\alpha )=\beta } is