منابع مشابه
Simple Complete Boolean Algebras
For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators.
متن کاملComplete Ccc Boolean Algebras
Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B, τs) is topologically dense. 2. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B, τ...
متن کاملComplete Quotient Boolean Algebras
For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...
متن کامل2 2 Ju n 20 04 SIMPLE COMPLETE BOOLEAN ALGEBRAS
For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators.
متن کاملA Note on Complete Boolean Algebras
1. Introduction. Among commutative rings, Boolean algebras stand just below fields in simplicity of structure. In contrast, little is known concerning their classification. The purpose of this paper is to present a decomposition theorem for complete Boolean algebras, which, in a small way, simplifies the classification problem. As an illustration of how this decomposition theorem can be used, i...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 1974
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02758124