Results 211 to 220 of about 945 (231)

Regular subalgebras of complete Boolean algebras

Journal of Symbolic Logic, 2001
AbstractIt is proved that the following conditions are equivalent:(a) there exists a complete, atomless, σ–centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra.(b) there exists a nowhere dense ultrafilter on ω.Therefore, the existence of such algebras is undecidable in ZFC.
Aleksander Blaszczyk, Saharon Shelah
openaire   +2 more sources

$ \alpha $ -cut-complete Boolean algebras

Algebra Universalis, 1998
Let \(A\) be a Boolean algebra and \(\alpha \) an infinite cardinal. An \(\alpha \)-cut in \(A\) is a pair \((F,H)\) of subsets of \(A\), each of size less than \(\alpha \), with \(F\leq H\) elementwise and with 0 as the meet of differences \(h-f\) for \(h\in H\), \(f\in F\). \(A\) is \(\alpha \)-cut-complete if for each \(\alpha \)-cut \((F,H)\) there
openaire   +1 more source

Precipitousness of a Sum of Ideals on Complete Boolean Algebras

Mathematical Logic Quarterly, 1988
\textit{T. Jech} and \textit{K. Prikry} [Mem. Am. Math. Soc. 214 (1979; Zbl 0398.03044)] introduced the notion of precipitousness for ideals on power set algebras. This notion is closely connected with well-foundedness of generic ultrapowers of models of set theory.
Joji Takahashi, Kazuaki Kajitori
openaire   +1 more source

Quotients of Complete Boolean Algebras

Annals of the New York Academy of Sciences, 1996
ABSTRACTWe show that every k‐field of sets with k > 2ω0 is a quotient of a complete Boolean algebra.
openaire   +1 more source

Partition Complete Boolean Algebras and Almost Compact Cardinals

Mathematical Logic Quarterly, 1999
Peter Jipsen
exaly  

On free subalgebras of complete Boolean algebras

Archiv Der Mathematik, 1977
J Donald Monk
exaly  

Free subalgebras of complete boolean algebras and spaces of continuous functions

Siberian Mathematical Journal, 1974
S V Kislyakov, Kislyakov S V
exaly  

A note on complete partitions in boolean algebras

Mathematical Logic Quarterly, 1990
openaire   +1 more source

Completing Boolean Algebras by Nonstandard Methods

Mathematical Logic Quarterly, 1974
openaire   +2 more sources

Boolean Algebras, Tarski Invariants, and Index Sets

Notre Dame Journal of Formal Logic, 2006
Barbara F Csima, Antonio Montalbán, Richard A Shore   +2 more
exaly