Files in this item
Files  Description  Format 

application/pdf 1_Tellez_Hernando.pdf (683kB)  (no description provided) 
Description
Title:  Contributions to model theory of metric structures 
Author(s):  Tellez, Hernando 
Director of Research:  Henson, C. Ward 
Doctoral Committee Chair(s):  Solecki, Slawomir 
Doctoral Committee Member(s):  Henson, C. Ward; van den Dries, Lou; Rosendal, Christian 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Continuous logic
Metric structures Model theory Perturbations Banach spaces Algebraic closure 
Abstract:  Two Banach spaces X and Y are said to be almost isometric if for every λ > 1 there exists a λisomorphism 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 RyllNardzewskistyle characterization of ωcategoricity 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 singlesorted 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. 
Issue Date:  20100519 
URI:  http://hdl.handle.net/2142/16109 
Rights Information:  Copyright 2010 Hernando Tellez 
Date Available in IDEALS:  20100519 
Date Deposited:  201005 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Mathematics