2026-09-19T13:23:38Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/29825 2023-07-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Henson, C. Ward Solecki, Slawomir Henson, C. Ward van den Dries, Lou Sowers, Richard B. Song, Shichang 2012-02-06T20:19:45Z 2012-02-06T20:19:45Z 2012-02-06T20:19:45Z 2011-12 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-09-07T20:16:52Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 Song_Shichang.pdf: 1283398 bytes, checksum: d43bee9461cf60ccd7104ff35e095af1 (MD5) Song_Shichang.tex: 494028 bytes, checksum: 6d62e4cece5df211a72ac0077e14af79 (MD5) Song_Shichang.pdf: 1282495 bytes, checksum: 4898c7b6c31e3d5065ddeb9a9c277348 (MD5) Made available in DSpace on 2012-02-06T20:19:45Z (GMT). No. of bitstreams: 3 Song_Shichang.pdf: 1283830 bytes, checksum: a092d9be5cc942b08350d79ce722708b (MD5) license.txt: 4061 bytes, checksum: 5f927f740dccd1c161929c940defa9f7 (MD5) Song_Shichang.tex: 496105 bytes, checksum: a933a6c01812ada763643dfb7b563c52 (MD5) http://hdl.handle.net/2142/29825 en Copyright 2011 Shichang Song Model theory continuous logic probability algebras random variables adapted spaces Model theory and probability Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD