Director of Research (if dissertation) or Advisor (if thesis)
van den Dries, Lou
Doctoral Committee Chair(s)
Hieronymi, Philipp
Committee Member(s)
Pillay, Anand
Tserunyan, Anush
Walsberg, Erik
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
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.
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