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Master's Dissertation
DOI
10.11606/D.45.2012.tde-01022013-171949
Document
Author
Full name
Rodrigo Figueiredo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Bianconi, Ricardo (President)
Coniglio, Marcelo Esteban
Mariano, Hugo Luiz
Title in Portuguese
Um resultado geral de modelo completude de expansões do corpo ordenado dos reais
Keywords in Portuguese
estrutura fraca o-minimal
estrutura o-minimal
expansão do corpo ordenado dos reais
fecho Charbonnel
lógica
teoria dos modelos
teoria modelo completa
Abstract in Portuguese
Este trabalho tem como foco principal estabelecer condições gerais suficientes para que uma expansão do corpo ordenado dos reais por funções com domínio em Rn seja modelo completa e o-minimal. Para tanto, faremos uma abordagem sob o ponto de vista de estruturas fracas o-minimais, conforme o trabalho de Charbonnel e Wilkie. Além disso, ao analisar condições adicionais, podemos obter a seguinte generalização de um trabalho de Gabrielov: uma expansão o-minimal do corpo ordenado dos reais por funções C infinito restritas, que é polinomialmente limitada e fechada sob diferenciação parcial, é modelo completa.
Title in English
A general model completeness result for expansions of the real ordered field
Keywords in English
Charbonnel closure
expansion of the real ordered field
logic
model complete theory
model theory
o-minimal structure
Abstract in English
The main focus of this dissertation lies in establishing some general sufficient conditions for an expansion of the real ordered field by functions with domains Rn to be model complete and o-minimal. We approach this subject from the point of view of the o-minimal weak structures, by following the work of Charbonnel and Wilkie. Furthermore, when considering additional conditions, we are able to obtain the following generalization of a Gabrielovs result: an expansion of the real ordered field by restricted smooth functions, which is polynomially bounded and closed under partial differentiation, is model complete.
 
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Publishing Date
2013-02-27
 
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