A Boolean model of ultrafilters

Annals of Pure and Applied Logic 99 (1-3):231-239 (1999)
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Abstract

We introduce the notion of Boolean measure algebra. It can be described shortly using some standard notations and terminology. If B is any Boolean algebra, let BN denote the algebra of sequences , xn B. Let us write pk BN the sequence such that pk = 1 if i K and Pk = 0 if k < i. If x B, denote by x* BN the constant sequence x* = . We define a Boolean measure algebra to be a Boolean algebra B with an operation μ:BN → B such that μ = 0 and μ = x. Any Boolean measure algebra can be used to model non-principal ultrafilters in a suitable sense. Also, we can build effectively the initial Boolean measure algebra. This construction is related to the closed open Ramsey Theorem 193–198.)

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Citations of this work

Forcing in proof theory.Jeremy Avigad - 2004 - Bulletin of Symbolic Logic 10 (3):305-333.
Intuitionistic choice and classical logic.Thierry Coquand & Erik Palmgren - 2000 - Archive for Mathematical Logic 39 (1):53-74.

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References found in this work

Lectures on Boolean Algebras.Paul R. Halmos - 1966 - Journal of Symbolic Logic 31 (2):253-254.
Borel sets and Ramsey's theorem.Fred Galvin & Karel Prikry - 1973 - Journal of Symbolic Logic 38 (2):193-198.
La logique Des topos.André Boileau & André Joyal - 1981 - Journal of Symbolic Logic 46 (1):6-16.
Constructive Sheaf Semantics.Erik Palmgren - 1997 - Mathematical Logic Quarterly 43 (3):321-327.
Intuitionistic choice and classical logic.Thierry Coquand & Erik Palmgren - 2000 - Archive for Mathematical Logic 39 (1):53-74.

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