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Title:Model theory of partially random structures
Author(s):Tran, Minh Chieu
Director of Research:van den Dries, Lou
Doctoral Committee Chair(s):Hieronymi, Philipp
Doctoral Committee Member(s):Pillay, Anand; Tserunyan, Anush; Walsberg, Erik
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Model theory
Random structures
Abstract:Many interactions between mathematical objects, e.g. the interaction between the set of primes and the additive structure of N, can be usefully thought of as random modulo some obvious obstructions. In the first part of this thesis, we document several such situations, show that the randomness in these interactions can be captured using first-order logic, and deduce in consequence many model-theoretic properties of the corresponding structures. The second part of this thesis develops a framework to study the aforementioned situations uniformly, shows that many examples of interest in model theory fit into this framework, and recovers many known model-theoretic phenomena about these examples from our results.
Issue Date:2019-07-12
Rights Information:Copyright 2019 Chieu-Minh Tran
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08

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