منابع مشابه
On Depth and Depth+ of Boolean Algebras
We show that the Depth of an ultraproduct of Boolean Algebras cannot jump over the Depth of every component by more than one cardinal. Consequently we have similar results for the Depth invariant.
متن کاملDepth of Boolean Algebras
Suppose D is an ultrafilter on κ and λ = λ. We prove that if Bi is a Boolean algebra for every i < κ and λ bounds the Depth of every Bi, then the Depth of the ultraproduct of the Bi’s mod D is bounded by λ. We also show that for singular cardinals with small cofinality, there is no gap at all. This gives a partial answer to problem No. 12 in [?]. 2000 Mathematics Subject Classification. Primary...
متن کاملDepth Zero Boolean Algebras
We study the class of depth zero Boolean algebras, both from a classical viewpoint and an effective viewpoint. In particular, we provide an algebraic characterization, constructing an explicit measure for each depth zero Boolean algebra and demonstrating there are no others, and an effective characterization, providing a necessary and sufficient condition for a depth zero Boolean algebra of ran...
متن کاملDepth+ and Length+ of Boolean Algebras
Suppose κ = cf(κ), λ > cf(λ) = κ and λ = λ. We prove that there exist a sequence 〈Bi : i < κ〉 of Boolean algebras and an ultrafilterD on κ so that λ = ∏ i<κ Depth(Bi)/D < Depth ( ∏ i<κ Bi/D) = λ . An identical result holds also for Length. The proof is carried in ZFC, and it holds even above large cardinals. 2010 Mathematics Subject Classification. Primary: 06E05, 03G05. Secondary: 03E45.
متن کاملOn Tightness and Depth in Superatomic Boolean Algebras
We introduce a large cardinal property which is consistent with L and show that for every superatomic Boolean algebra B and every cardinal λ with the large cardinal property, if tightness+(B) ≥ λ+, then depth(B) ≥ λ. This improves a theorem of Dow and Monk. In [DM, Theorem C], Dow and Monk have shown that if λ is a Ramsey cardinal (see [J, p.328]), then every superatomic Boolean algebra with ti...
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2008
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-008-2065-1