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Displaying similar documents to “Cellularity of free products of Boolean algebras (or topologies)”

Prenormality of ideals and completeness of their quotient algebras

A. Morawiec, B. Węglorz (1993)

Colloquium Mathematicae

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It is well known that if a nontrivial ideal ℑ on κ is normal, its quotient Boolean algebra P(κ)/ℑ is κ + -complete. It is also known that such completeness of the quotient does not characterize normality, since P(κ)/ℑ turns out to be κ + -complete whenever ℑ is prenormal, i.e. whenever there exists a minimal ℑ-measurable function in κ κ . Recently, it has been established by Zrotowski (see [Z1], [CWZ] and [Z2]) that for non-Mahlo κ, not only is the above condition sufficient but also necessary...

Stability of the 4-2 Binary Addition Circuit Cells. Part I

Katsumi Wasaki (2008)

Formalized Mathematics

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To evaluate our formal verification method on a real-size calculation circuit, in this article, we continue to formalize the concept of the 4-2 Binary Addition Cell primitives (FTAs) to define the structures of calculation units for a very fast multiplication algorithm for VLSI implementation [11]. We define the circuit structure of four-types FTAs, TYPE-0 to TYPE-3, using the series constructions of the Generalized Full Adder Circuits (GFAs) that generalized adder to have for each positive...

The smallest common extension of a sequence of models of ZFC

Lev Bukovský, Jaroslav Skřivánek (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we show that the model obtained by finite support iteration of a sequence of generic extensions of models of ZFC of length ω is sometimes the smallest common extension of this sequence and very often it is not.

On a problem of Steve Kalikow

Saharon Shelah (2000)

Fundamenta Mathematicae

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The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for ℵ ω but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants. ...

Properties of forcing preserved by finite support iterations

Miroslav Repický (1991)

Commentationes Mathematicae Universitatis Carolinae

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We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.