{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86816"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86816","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"T-Levels and T-Convexity","abstract":"\"Let R be a model of an o-minimal theory T. We define the \"\"T-levels\"\" of R and explore their connection to tame substructures of R , subject to a few easily satisfied assumptions. This leads to results about the theory of models of T equipped with a T-convex subset, and to answers to some open questions about o-minimal expansions of real closed fields equipped with a T-convex subring. Specifically, we establish the Valuation and Residue Properties for power bounded o-minimal expansions of real closed fields equipped with a T-convex subring.\"","abstract_html":""Let R be a model of an o-minimal theory T. We define the ""T-levels"" of R and explore their connection to tame substructures of R , subject to a few easily satisfied assumptions. This leads to results about the theory of models of T equipped with a T-convex subset, and to answers to some open questions about o-minimal expansions of real closed fields equipped with a T-convex subring. 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