On weak convergence of measures and σ-complete Boolean algebras
نویسندگان
چکیده
منابع مشابه
On the weak Freese-Nation property of complete Boolean algebras
The following results are proved: (a) In a model obtained by adding א2 Cohen reals, there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. (b) Modulo the consistency strength of a supercompact cardinal, the existence of a c.c.c. complete Boolean algebra without the weak Freese-Nation property is consistent with GCH. (c) If a weak form of 2μ and cof([μ] א0 ,⊆)...
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Let convergences λi : B → P (B), i ≤ 4, on a complete Boolean algebra B be defined in the following way. For a sequence x = 〈xn : n ∈ ω〉 in B and the corresponding B-name for a subset of ω, τx = {〈ň, xn〉 : n ∈ ω}, let λi(x) = { {‖τx is infinite‖} if bi(x) = 1B, ∅ otherwise, where b1(x) = ‖τx is finite or cofinite‖, b2(x) = ‖τx is not unsupported‖, b3(x) = ‖τx is not a splitting real‖ and b4(x) ...
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We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
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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 ...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1964
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-12-2-229-233