2026-09-21T19:52:25Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/16109 2023-07-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Continuous logic 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) http://hdl.handle.net/2142/16109 Henson, C. Ward Solecki, Slawomir Henson, C. Ward van den Dries, Lou Rosendal, Christian Tellez, Hernando 2010-05-19T18:36:29Z 2010-05-19T18:36:29Z 2010-05-19T18:36:29Z 2010-05 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 Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2010-01-03T21:31:15Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of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) en Copyright 2010 Hernando Tellez Metric structures Model theory Perturbations Banach spaces Algebraic closure Contributions to model theory of metric structures Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD