More on regular and decomposable ultrafilters in ZFC
نویسندگان
چکیده
منابع مشابه
More Results on Regular Ultrafilters in Zfc
We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters; among them: (a) If m ≥ 1 and the ultrafilter D is (im(λ),im(λ))regular then D is κ-decomposable for some κ with λ ≤ κ ≤ 2 (Theorem 4.3(a)). (b) If λ is a strong limit cardinal and D is (im(λ ),im(λ ))regular then either D is (cf λ, cf λ)-regular or there are arbitrarily large κ < λ for which D is κ-decom...
متن کاملDecomposable Ultrafilters and Possible Cofinalities
We use Shelah’s theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem 1. Suppose that λ is a singular cardinal, λ′ < λ, and the ultrafilter D is κ-decomposable for all regular cardinals κ with λ′ < κ < λ. Then D is either λ-decomposable, or λ-decomposable. Corollary 2. If λ is a singular cardinal, then an ultrafilter is (λ, λ)-regular if and only if it is e...
متن کاملRegular ultrafilters and finite square principles
We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle ¤ λ,D introduced in [3]. For such ultrafilters D and cardinals λ Research partially supported by a grant from NWO and grant 40734 of the Academy of Finland. The second author would like to thank the Israel Science Foundation for partial support of this re...
متن کاملMatroid Secretary for Regular and Decomposable Matroids
In the matroid secretary problem we are given a stream of elements in random order and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable: if we choose to accept an element when it is presented by the stream then we can never get ri...
متن کاملRegular languages of plus - and minus - ( in ) decomposable permutations
In this paper we show that the sets of plusrespectively minus-decomposable permutations of a regular class under the rank encoding form regular sublanguages. Plusrespectively minus-decomposable permutations are permutations allowing for a special kind of block-decomposition. The language theoretic results shown have di erent approaches, even though the properties of plusand minus-decomposabilit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 2010
ISSN: 0942-5616
DOI: 10.1002/malq.200910013