A model in which every Boolean algebra has many subalgebras

Journal of Symbolic Logic 60 (3):992-1004 (1995)
We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2 |A| = 2 |B| . This implies in particular that B has 2 |B| subalgebras. We also discuss some more general problems about subalgebras and free subsets of an algebra. The result on the number of subalgebras in a Boolean algebra solves a question of Monk from [6]. The paper is intended to be accessible as far as possible to a general audience, in particular we have confined the more technical material to a "black box" at the end. The proof involves a variation on Foreman and Woodin's model in which GCH fails everywhere
Keywords Boolean algebras   free subsets   Radin forcing
Categories (categorize this paper)
DOI 10.2307/2275769
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 35,865
Through your library

References found in this work BETA

Adding Closed Cofinal Sequences to Large Cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243-261.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles


Added to PP index

Total downloads
10 ( #530,175 of 2,293,838 )

Recent downloads (6 months)
3 ( #182,717 of 2,293,838 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature