2026-09-20T15:29:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/105670 2023-07-11 col_2142_16340 col_2142_5131 com_2142_16339 com_2142_8903 com_2142_5130

van den Dries, Lou Hieronymi, Philipp Pillay, Anand Tserunyan, Anush Walsberg, Erik Tran, Minh Chieu 2019-11-26T20:35:00Z 2019-11-26T20:35:00Z 2019-07-12 2019-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms The student, Minh Tran, accepted the attached license on 2019-07-10 at 14:09. The student, Minh Tran, submitted this Dissertation for approval on 2019-07-10 at 14:22. This Dissertation was approved for publication on 2019-07-12 at 16:45. DSpace SAF Submission Ingestion Package generated from Vireo submission #14247 on 2019-11-26 at 12:52:18 Made available in DSpace on 2019-11-26T20:35:00Z (GMT). No. of bitstreams: 2 TRAN-DISSERTATION-2019.pdf: 1354314 bytes, checksum: 42df7a5e27b8adfd5530c2c7075bdfd7 (MD5) LICENSE.txt: 4206 bytes, checksum: 3f239d8e674e1019f89da6fc8c3f705e (MD5) Previous issue date: 2019-07-12 application/pdf http://hdl.handle.net/2142/105670 en Copyright 2019 Chieu-Minh Tran Model theory Random structures Model theory of partially random structures text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.