More constructions for Boolean algebras

Saharon Shelah

doi:10.1007/s001530100099

More constructions for Boolean algebras

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

4 Scopus citations

Abstract

We construct Boolean algebras with prescribed behaviour concerning depth for the free product of two Boolean algebras over a third, in ZFC using pcf; assuming squares we get results on ultraproducts. We also deal with the family of cardinalities and topological density of homomorphic images of Boolean algebras (you can translate it to topology - on the cardinalities of closed subspaces); and lastly we deal with inequalities between cardinal invariants, mainly d(B)^k < |B| ⇒ ind(B) > κ ∨ Depth(B) ≥ log(|B|).

Original language	English
Pages (from-to)	401-441
Number of pages	41
Journal	Archive for Mathematical Logic
Volume	41
Issue number	5
DOIs	https://doi.org/10.1007/s001530100099
State	Published - Jul 2002

Keywords

Boolean algebras
Cardinal invariants of Boolean algebras
Depth of Boolean algebra
Forcing
PCF application
Set theory
ZFC constructions

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10.1007/s001530100099

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KW - Boolean algebras

KW - Cardinal invariants of Boolean algebras

KW - Depth of Boolean algebra

KW - Forcing

KW - PCF application

KW - Set theory

KW - ZFC constructions

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More constructions for Boolean algebras

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