## Journal of Symbolic Logic

### On some small cardinals for Boolean algebras

#### 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].

#### Article information

Source
J. Symbolic Logic, Volume 69, Issue 3 (2004), 674-682.

Dates
First available in Project Euclid: 4 October 2004

https://projecteuclid.org/euclid.jsl/1096901761

Digital Object Identifier
doi:10.2178/jsl/1096901761

Mathematical Reviews number (MathSciNet)
MR2078916

Zentralblatt MATH identifier
1077.03027

#### Citation

McKenzie, Ralph; Monk, J. Donald. On some small cardinals for Boolean algebras. J. Symbolic Logic 69 (2004), no. 3, 674--682. doi:10.2178/jsl/1096901761. https://projecteuclid.org/euclid.jsl/1096901761

#### References

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