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http://hdl.handle.net/11375/21442
Title: | Continuous Model Theory and Finite-Representability Between Banach Spaces |
Authors: | Conley, Sean |
Advisor: | Hart, Bradd |
Department: | Mathematics |
Keywords: | logic;continuous model theory |
Publication Date: | May-2017 |
Abstract: | In this thesis, we consider the problem of capturing finite-representability between Banach spaces using the tools of continuous model theory. We introduce predicates and additional sorts to capture finite-representability and show that these can be used to expand the language of Banach spaces. We then show that the class of infinite-dimensional Banach spaces expanded with this additional structure forms an elementary class K_G , and conclude that the theory T_G of K_G is interpretable in T^{eq} , where T is the theory of infinite-dimensional Banach spaces. Finally, we show that existential equivalence in a reduct of the language implies finite-representability. Relevant background on continuous model theory and Banach space theory is provided. |
URI: | http://hdl.handle.net/11375/21442 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Conley_Sean_T_201704_MSc.pdf | 335.06 kB | Adobe PDF | View/Open |
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