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A saturation property of structures obtained by forcing with a compact family of random variables

A saturation property of structures obtained by forcing with a compact family of random variables A method for constructing Boolean-valued models of some fragments of arithmetic was developed in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family [called compactness in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011)] the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

A saturation property of structures obtained by forcing with a compact family of random variables

Archive for Mathematical Logic , Volume 52 (2) – Sep 13, 2012

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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer-Verlag
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-012-0304-9
Publisher site
See Article on Publisher Site

Abstract

A method for constructing Boolean-valued models of some fragments of arithmetic was developed in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family [called compactness in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011)] the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Sep 13, 2012

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