Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-22T21:18:59.262Z Has data issue: false hasContentIssue false
  • English
  • Français

WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

Published online by Cambridge University Press:  29 June 2016

DAN HATHAWAY
DAN HATHAWAY*
Affiliation:
MATHEMATICS DEPARTMENTUNIVERSITY OF DENVERDENVER, CO80208, USAE-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Set Theorycomplete Boolean algebrasdistributive lawsweak distributivityweakly compact cardinalsthe tower number
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 711 - 717
Copyright
Copyright © The Association for Symbolic Logic 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
Jech, T., Set Theory, third ed., Springer, New York, NY, 2002. Revised and Expanded.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