Model theory and probability

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Song, Shichang

Contributors dc:contributor

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

• Model theory
• continuous logic
• probability algebras
• random variables
• adapted spaces

Statement dc:rights

• Copyright 2011 Shichang Song

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/29825