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. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21442 |
| Date | 05 1900 |
| Creators | Conley, Sean |
| Contributors | Hart, Bradd, Mathematics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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