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WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY
Published online by Cambridge University Press: 29 June 2016
Abstract
Let 
$B$ be a complete Boolean algebra. We show that if λ is an infinite cardinal and 
$B$ is weakly (λω, ω)-distributive, then 
$B$ is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that 
$B$ is weakly (2κ, κ)-distributive and 
$B$ is (α, 2)-distributive for each α < κ, then 
$B$ is (κ, 2)-distributive.
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- Copyright © The Association for Symbolic Logic 2016
References
REFERENCES
Blass, A.,
Combinatorial cardinal characteristics of the continuum
, Handbook of Set Theory (Foreman, M. and Kanamori, A., editors), vol. 1, Springer, New York, 2010, pp. 395–489.Google Scholar
Dordal, P., Towers in [ω]
ω
and
ω
ω. Annals of Pure and Applies Logic, vol. 45 (1989), pp. 247–276.Google Scholar
Farah, I.,
OCA and towers in P(N)/fin
. Commentationes Mathematicae Universitatis Carolinae, vol. 37 (1996), pp. 861–866.Google Scholar
Hathaway, D., A lower bound for generalized dominating numbers, arXiv:1401.7948.Google Scholar
Jech, T.,
Distributive laws
, Handbook of Boolean Algebra (Bonnet, R. and Monk, J.D., editors), North-Holland, Amsterdam, 1989.Google Scholar
Kamburelis, A.,
On the weak distributibity game
. Annals of Pure and Applied Logic, vol. 66 (1994), pp. 19–26.Google Scholar
Martin, D. and Solovay, R.,
Internal Cohen Extensions
. Annals of Mathematics, vol. 2 (1970), pp. 143–178.Google Scholar