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

, 1947
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Dense subtrees in complete Boolean algebras

Mathematical Logic Quarterly, 2006
AbstractWe characterize complete Boolean algebras with dense subtrees. The main results show that a complete Boolean algebra contains a dense tree if its generic filter collapses the algebra's density to its distributivity number and the reverse holds for homogeneous algebras. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bernhard KÖNIG
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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 ...
Miloš S Kurilić, Stevo Todorcevic, Kurilić Miloš S   +2 more
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On the number of complete boolean algebras

Algebra Universalis, 1972
Monk, J. Donald, Solovay, R. M.
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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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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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