Model theory of partially random structures

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.

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

2019

Author dc:creator

• Tran, Minh Chieu

Contributors dc:contributor

• van den Dries, Lou
• Hieronymi, Philipp
• Pillay, Anand
• Tserunyan, Anush
• Walsberg, Erik

• Model theory
• Random structures

Statement dc:rights

• Copyright 2019 Chieu-Minh Tran

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105670