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MODEL THEORY OF MEASURE SPACES AND PROBABILITY LOGIC

Published online by Cambridge University Press:  08 April 2013

RUTGER KUYPER  and
SEBASTIAAN A. TERWIJN
RUTGER KUYPER*
Affiliation:
Department of Mathematics, Radboud University Nijmegen
SEBASTIAAN A. TERWIJN*
Affiliation:
Department of Mathematics, Radboud University Nijmegen
*
*DEPARTMENT OF MATHEMATICS RADBOUD UNIVERSITY NIJMEGEN P.O. BOX 9010, 6500 GL NIJMEGEN, THE NETHERLANDS E-mail: [email protected], [email protected]
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Abstract

We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a certain class of weak models.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 3 , September 2013 , pp. 367 - 393
Copyright
Copyright © Association for Symbolic Logic 2013 

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