Model theory and probability

Song, Shichang

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https://hdl.handle.net/2142/29825 Copy

Description

Title

Model theory and probability

Author(s)

Song, Shichang

Issue Date

2012-02-06T20:19:45Z

Director of Research (if dissertation) or Advisor (if thesis)

Henson, C. Ward

Doctoral Committee Chair(s)

Solecki, Slawomir

Committee Member(s)

• Henson, C. Ward
• van den Dries, Lou
• Sowers, Richard B.

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2011-12

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http://hdl.handle.net/2142/29825

Copyright and License Information

Copyright 2011 Shichang Song

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