منابع مشابه
Depth 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 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 کاملOn 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+ 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 کاملThe Depth of Ultraproducts of Boolean Algebras Sh853
We show that if μ is a compact cardinal then the depth of ultraproducts of less than μ many Boolean Algebras is at most μ plus the ultraproduct of the depths of those Boolean Algebras. I would like to thank Alice Leonhardt for the beautiful typing. This research was supported by the United States-Israel Binational Science Foundation First Typed 03/Nov/14 Latest Revision 05/May/3 Typeset by AMS-...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-10-05002-6