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Model theory and probability

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Title: Model theory and probability
Author(s): Song, Shichang
Director of Research: Henson, Ward
Doctoral Committee Chair(s): Solecki, Slawomir
Doctoral Committee Member(s): Henson, Ward; van den Dries, Lou; Sowers, Richard
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Model theory continuous logic probability algebras random variables adapted spaces.
Abstract: This thesis presents a systematic study of the model theory of probability algebras, random variable structures, and adapted structures, with an emphasis on their atomless counterparts. In this thesis, the author uses a continuous version of first order logic that has been developed recently and that is better suited for applications to metric structures than classical first order logic. The set of truth values in continuous logic is the interval [0,1] instead of the truth values {True, False} in classical logic. The author studies axioms, type spaces, quantifier elimination, separable categoricity, saturated models, stability, and d-finiteness for the theories of atomless probability algebras and atomless random variable structures. Explicit formulas for the d*-metric between types in the theory of atomless random variable structures are given. For the theory of atomless adapted structures, the author studies axioms, type spaces, quantifier elimination, separably categoricity, and d-finiteness.
Issue Date: 2012-02-06
Rights Information: Copyright 2011 Shichang Song
Date Available in IDEALS: 2012-02-06
Date Deposited: 2011-12

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