Independent families in complete Boolean algebras-Reference-Cited by-同舟云学术

Independent families in complete Boolean algebras

Published:1982 Issue:2 Volume:274 Page:607-618
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Balcar B.,Franěk F.

Abstract

We present a proof (without any set-theoretical assumptions) that every infinite complete Boolean algebra includes a free subalgebra of the same cardinality. It follows that the set of all ultrafilters on an infinite complete Boolean algebra B B has power 2 | B | 2^{|B|} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1982-274-02/S0002-9947-1982-0675069-3/S0002-9947-1982-0675069-3.pdf

Reference27 articles.

1. M. Benda, Reduced products, filters and Boolean ultrapowers, Ph.D. Thesis, University of Wisconsin, 1970.

2. Refining systems on Boolean algebras;Balcar, Bohuslav,1977

3. A. Blaszczyk, On mappings of extremally disconnected compact spaces onto Cantor cubes, Proc. Colloq. Topology, Budapest, 1978.

4. L. Bukovsky, Boolean ultrapowers and elementary equivalence, Abstract of 4th ICLMPS Bucharest, 1971, pp. 13-14.

5. Cardinality of 𝔨-complete Boolean algebras;Comfort, W. W.;Pacific J. Math.,1972

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