University of Illinois Urbana-Champaign

Model theory of partially random structures

Tran, Minh Chieu

Content Files
TRAN-DISSERTATION-2019.pdf

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https://hdl.handle.net/2142/105670

Description

Title
Model theory of partially random structures
Author(s)
Tran, Minh Chieu
Issue Date
2019-07-12
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
Date of Ingest
2019-11-26T20:35:00Z
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.
Graduation Semester
2019-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/105670
Copyright and License Information
Copyright 2019 Chieu-Minh Tran

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