Depth+ and length+ of boolean algebras

Shimon Garti; Saharon Shelah

Depth⁺ and length⁺ of boolean algebras

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose that κ = cf(κ), λ > cf(λ) = κ⁺ and λ = λ^κ. We prove that there exist a sequence hB_i : i < κi of Boolean algebras and an ultrafilter D over κ so that λ = Q Depth⁺(B_i)/D < Depth⁺(Q B_i/D) = λ⁺. An i<κ i<κ identical result holds also for Length⁺. The proof is carried in ZFC, and it holds even above large cardinals.

Original language	American English
Pages (from-to)	953-963
Number of pages	11
Journal	Houston Journal of Mathematics
Volume	45
Issue number	4
State	Published - 1 Jan 2019
Externally published	Yes

Keywords

Boolean algebras
Depth
Ultraproducts

All Science Journal Classification (ASJC) codes

General Mathematics

Cite this

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title = "Depth+ and length+ of boolean algebras",

abstract = "Suppose that κ = cf(κ), λ > cf(λ) = κ+ and λ = λκ. We prove that there exist a sequence hBi : i < κi of Boolean algebras and an ultrafilter D over κ so that λ = Q Depth+(Bi)/D < Depth+(Q Bi/D) = λ+. An i<κ i<κ identical result holds also for Length+. The proof is carried in ZFC, and it holds even above large cardinals.",

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AU - Garti, Shimon

AU - Shelah, Saharon

PY - 2019/1/1

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N2 - Suppose that κ = cf(κ), λ > cf(λ) = κ+ and λ = λκ. We prove that there exist a sequence hBi : i < κi of Boolean algebras and an ultrafilter D over κ so that λ = Q Depth+(Bi)/D < Depth+(Q Bi/D) = λ+. An i<κ i<κ identical result holds also for Length+. The proof is carried in ZFC, and it holds even above large cardinals.

AB - Suppose that κ = cf(κ), λ > cf(λ) = κ+ and λ = λκ. We prove that there exist a sequence hBi : i < κi of Boolean algebras and an ultrafilter D over κ so that λ = Q Depth+(Bi)/D < Depth+(Q Bi/D) = λ+. An i<κ i<κ identical result holds also for Length+. The proof is carried in ZFC, and it holds even above large cardinals.

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KW - Depth

KW - Ultraproducts

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M3 - Article

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JO - Houston Journal of Mathematics

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