Depth+ and Length+ of Boolean Algebras
نویسنده
چکیده
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.
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تاریخ انتشار 2013