Results 181 to 190 of about 1,728 (218)

On the representation of \(\sigma\)-complete Boolean algebras

, 1947
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A Complete Boolean Algebra That Has No Proper Atomless Complete Subalgebra

Journal of Algebra, 1996
There exists a complete atomless Boolean algebra that has no proper atomless complete ...
Thomas Jech, Saharon Shelah
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Embedding of free Boolean algebras in complete Boolean algebras

Journal of Soviet Mathematics, 1975
S V Kislyakov, Kislyakov S V
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Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra

European Journal of Mathematics
Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown to exist within a larger framework involving BCK-algebras of functions, whose ideals and prime ideals ...
Charles Matthew Evans
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On Boolean Algebras and their Recursive Completions

Mathematical Logic Quarterly, 1985
Let B be a countable atomless Boolean algebra with a fixed bijective indexing \(\phi\) : \(\omega\to B\) such that the induced operations on \(\omega\) are recursive. An automorphism of B is said to be recursively presented if the induced permutation of \(\omega\) is recursive.
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On measures on complete Boolean algebras

Journal of Symbolic Logic, 1971
In this paper we prove some theorems concerning measures on complete Boolean algebras. Among other things, in §I of this paper, we construct a counterexample to the following conjecture of W. Luxemburg: Every measure on a nonatomic hyperstonian Boolean algebra is normal. (See [3, p. 57].) This result is expressed by Theorem 1, §I. In order to construct
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The Completion of a Boolean Algebra

1973
For the following let X be a topological space, and let S ⊆ X be a subspace of X with the relative topology. The topological operations -, ° and -s, os refer to X and S respectively.
Gaisi Takeuti, Wilson M. Zaring
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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
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Property $${(\hbar)}$$ and cellularity of complete Boolean algebras

Archive for Mathematical Logic, 2009
A complete Boolean algebra \(\mathbf B\) satisfies property \({(\hbar)}\) if and only if each sequence \(x\) in \(\mathbf B\) has a subsequence \(y\) such that the equality \(\limsup z_{n} = \limsup y_n\) holds for each subsequence \(z\) of \(y\). The class of complete Boolean algebras satisfying property \({(\hbar)}\) includes all finite algebras as ...
Milos S. Kurilic, Stevo Todorcevic
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$ \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
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