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On some small cardinals for Boolean algebras

Published online by Cambridge University Press:  12 March 2014

Ralph Mckenzie  and
J. Donald Monk
Ralph Mckenzie
Affiliation:
Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA, E-mail: mckenzie@math.vanderbilt.edu
J. Donald Monk
Affiliation:
Department of Mathematics, 395UCB, University of Colorado, Boulder, CO 80309-0395, USA, E-mail: monkd@euclid.colorado.edu
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Abstract.

Assume that all algebras are atomless. (1) Spind(A × B) = Spind(A) ∪ Spind(B). (2) 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 t(A) = s(A) = κ and α (A) = λ. All results are in ZFC, and answer some problems posed in Monk [01] and Monk [∞].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 674 - 682
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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