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September 2004 On some small cardinals for Boolean algebras
Ralph McKenzie, J. Donald Monk
J. Symbolic Logic 69(3): 674-682 (September 2004). DOI: 10.2178/jsl/1096901761

Abstract

Assume that all algebras are atomless. (1) Spind(A× B)=Spind(A)∪ Spind(B). (2) Spind(∏wi∈ IAi)={ω}∪⋃i∈ I Spind (Ai). Now suppose that κ and λ are infinite cardinals, with κ uncountable and regular and with κ<λ. (3) There is an atomless Boolean algebra A such that 𝔲(A)=κ and 𝔦(A)=λ. (4) If λ is also regular, then there is an atomless Boolean algebra A such that 𝔰(A)=𝔰(A)=κ and 𝔞(A)=λ. All results are in ZFC, and answer some problems posed in Monk [Mon01] and Monk [MonInf].

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Ralph McKenzie. J. Donald Monk. "On some small cardinals for Boolean algebras." J. Symbolic Logic 69 (3) 674 - 682, September 2004. https://doi.org/10.2178/jsl/1096901761

Information

Published: September 2004
First available in Project Euclid: 4 October 2004

zbMATH: 1077.03027
MathSciNet: MR2078916
Digital Object Identifier: 10.2178/jsl/1096901761

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 3 • September 2004
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