On some small cardinals for Boolean algebras
Ralph McKenzie and J. Donald Monk
Source: J. Symbolic Logic
Volume 69, Issue 3
(2004), 674-682.
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1096901761
Mathematical Reviews number (MathSciNet):
MR2078916
Digital Object Identifier: doi:10.2178/jsl/1096901761
Zentralblatt MATH identifier:
1077.03027
References
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Mathematical Reviews (MathSciNet):
MR991597
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Mathematical Reviews (MathSciNet):
MR879489
S. Koppelberg General theory of Boolean algebras, Handbook of Boolean algebras. Vol. 1 (R. Bonnet and D. Monk, editors), North-Holland, Amsterdam ,1989.
Mathematical Reviews (MathSciNet):
MR991595
J. D. Monk Continuum cardinals generalized to Boolean algebras, Journal of Symbolic Logic, vol. 66 (2001), no. 4, pp. 1928--1958.
