Os fundamentos do pensamento matematico no seculo XX e a relevancia fundacional da teoria de modelos / The foudations of mathematical thought in the twentieth century and the foundational relevance of model theory

AUTOR(ES)

Rodrigo de Alvarenga Freire

DATA DE PUBLICAÇÃO

2009

RESUMO

The aim of the present Thesis is to bring some light to the question about the status and relevance of Model Theory to a reflection about the mathematical knowledge in the twentieth century. To pursue this target, we will, first of all, try to reach a comprehension of the reflection about the mathematical knowledge, itself, what will be designated as Foundations of Mathematical Thought in the twentieth century, and of the foundational relevance, itself. In the sequel, we will provide an analysis, of the role of Model Theory and its interaction with Algebra, in general, within the established foundational setting and, finally, we will discuss a specific study case. In this study case we will show that Galois Theory can be seen as a logical content, and we will try to understand the foundational meaning of this model-theoretic framework for some part of classical Algebra

ASSUNTO(S)

matematica - filosofia teoria dos modelos logic mathematics symbolic and mathematical galois theory matematica - fundamentos teoria de galois lógica simbólica e matemática model theory mathematics

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