On some small cardinals for Boolean algebras
McKenzie, Ralph ; Monk, J. Donald
J. Symbolic Logic, Tome 69 (2004) no. 1, p. 674-682 / Harvested from Project Euclid
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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].
Publié le : 2004-09-14
Classification:  
@article{1096901761,
     author = {McKenzie, Ralph and Monk, J. Donald},
     title = {On some small cardinals for Boolean algebras},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 674-682},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1096901761}
}

McKenzie, Ralph; Monk, J. Donald. On some small cardinals for Boolean algebras. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  674-682. http://gdmltest.u-ga.fr/item/1096901761/