{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16109"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16109","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Contributions to model theory of metric structures","abstract":"Made available in DSpace on 2010-05-19T18:36:29Z (GMT). No. of bitstreams: 3 Tellez_Hernando.pdf: 683026 bytes, checksum: 63aec6056aa460a185790c297edd2ee9 (MD5) 1_Tellez_Hernando.pdf: 683016 bytes, checksum: 1498cf52175b63f07a8ffcf6f6c61998 (MD5) license.txt: 4064 bytes, checksum: f69d29af1b13351e842e978c04bfaeba (MD5)","abstract_html":"Made available in DSpace on 2010-05-19T18:36:29Z (GMT). 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No. of bitstreams: 3 Tellez_Hernando.pdf: 683026 bytes, checksum: 63aec6056aa460a185790c297edd2ee9 (MD5) 1_Tellez_Hernando.pdf: 683016 bytes, checksum: 1498cf52175b63f07a8ffcf6f6c61998 (MD5) license.txt: 4064 bytes, checksum: f69d29af1b13351e842e978c04bfaeba (MD5)","Two Banach spaces X and Y are said to be almost isometric if for every λ > 1 there exists a λ-isomorphism f : X → Y . That is, a linear surjective map such that 1/λ ∥x∥ ≤ ∥f (x)∥ ≤ λ ∥x∥ for every x ∈ X . In this thesis we prove a Ryll-Nardzewski-style characterization of ω-categoricity up to almost isometry for Banach spaces using the concept of perturbations of metric structures and tools developed by Ben Yaacov ([6] and [5]). To this end we construct a single-sorted signature Lc for the study of the model theory of Banach spaces in the setting of continuous first order logic, we give an explicit axiomatization for the class of Lc -structures that come from unit balls of Banach spaces and we construct a perturbation system that is adequate for the study of almost isometric Banach spaces. Additionally, we study the algebraic closure construction for metric structures in the setting of continuous first order logic. We give several characterizations of algebraicity, and we prove basic properties analogous to ones that the algebraic closure satisfes in classical first order logic.","Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2010-01-03T21:31:15Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Tellez_Hernando.pdf: 683026 bytes, checksum: 63aec6056aa460a185790c297edd2ee9 (MD5)"]},{"key":"dc:title","label":"Title","values":["Contributions to model theory of metric structures"]}]}],"canonical_facts":{"dc:contributor":["Henson, C. Ward","Solecki, Slawomir","van den Dries, Lou","Rosendal, Christian"],"dc:creator":["Tellez, Hernando"],"dc:date":["2010-05-19T18:36:29Z","2010-05"],"dc:description":["Made available in DSpace on 2010-05-19T18:36:29Z (GMT). No. of bitstreams: 3 Tellez_Hernando.pdf: 683026 bytes, checksum: 63aec6056aa460a185790c297edd2ee9 (MD5) 1_Tellez_Hernando.pdf: 683016 bytes, checksum: 1498cf52175b63f07a8ffcf6f6c61998 (MD5) license.txt: 4064 bytes, checksum: f69d29af1b13351e842e978c04bfaeba (MD5)","Two Banach spaces X and Y are said to be almost isometric if for every λ > 1 there exists a λ-isomorphism f : X → Y . That is, a linear surjective map such that 1/λ ∥x∥ ≤ ∥f (x)∥ ≤ λ ∥x∥ for every x ∈ X . In this thesis we prove a Ryll-Nardzewski-style characterization of ω-categoricity up to almost isometry for Banach spaces using the concept of perturbations of metric structures and tools developed by Ben Yaacov ([6] and [5]). To this end we construct a single-sorted signature Lc for the study of the model theory of Banach spaces in the setting of continuous first order logic, we give an explicit axiomatization for the class of Lc -structures that come from unit balls of Banach spaces and we construct a perturbation system that is adequate for the study of almost isometric Banach spaces. Additionally, we study the algebraic closure construction for metric structures in the setting of continuous first order logic. We give several characterizations of algebraicity, and we prove basic properties analogous to ones that the algebraic closure satisfes in classical first order logic.","Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2010-01-03T21:31:15Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Tellez_Hernando.pdf: 683026 bytes, checksum: 63aec6056aa460a185790c297edd2ee9 (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/16109"],"dc:language":["en"],"dc:rights":["Copyright 2010 Hernando Tellez"],"dc:subject":["Continuous logic","Metric structures","Model theory","Perturbations","Banach spaces","Algebraic closure"],"dc:title":["Contributions to model theory of metric structures"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:08Z"}