Forcing minimal extensions of Boolean algebras
نویسندگان
چکیده
منابع مشابه
Forcing Minimal Extensions of Boolean Algebras
We employ a forcing approach to extending Boolean algebras. A link between some forcings and some cardinal functions on Boolean algebras is found and exploited. We find the following applications: 1) We make Fedorchuk’s method more flexible, obtaining, for every cardinal λ of uncountable cofinality, a consistent example of a Boolean algebra Aλ whose every infinite homomorphic image is of cardin...
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It was proved by Juhász and Weiss that for every ordinal α with 0 < α < ω2 there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that κ = κ and α is an ordinal such that 0 < α < κ++, then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1999
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-99-02145-5