منابع مشابه
Many simple cardinal invariants
For g < f in ω we define c(f, g) be the least number of uniform trees with g-splitting needed to cover a uniform tree with f -splitting. We show that we can simultaneously force א1 many different values for different functions (f, g). In the language of [Blass]: There may be א1 many distinct uniform Π1 characteristics. 0. Introduction [Blass] defined a classification of certain cardinal invaria...
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We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B0 × B1) = max{irr(B0), irr(B1)}. We prove consistency of the statement “there is a Boolean algebra B such that irr(B) < s(B ~ B)” and we force a superatomic Boolean algebra B∗ such that s(B∗) = inc(B∗) = κ, irr(B∗) ...
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Given an ideal I on ω let a(I) (ā(I)) be minimum of the cardinalities of in nite (uncountable) maximal I-almost disjoint subsets of [ω]. We show that a(Ih) > ω if Ih is a summable ideal; but a(Z~ μ) = ω for any tall density ideal Z~ μ including the density zero ideal Z. On the other hand, you have b ≤ ā(I) for any analytic P -ideal I, and ā(Z~ μ) ≤ a for each density ideal Z~ μ. For each ideal ...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2008
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-008-0094-2