Detalhes bibliográficos
| Ano de defesa: |
2007 |
| Autor(a) principal: |
Farias, Pablo Mayckon Silva |
| Orientador(a): |
Não Informado pela instituição |
| Banca de defesa: |
Não Informado pela instituição |
| Tipo de documento: |
Dissertação
|
| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Não Informado pela instituição
|
| Programa de Pós-Graduação: |
Não Informado pela instituição
|
| Departamento: |
Não Informado pela instituição
|
| País: |
Não Informado pela instituição
|
| Palavras-chave em Português: |
|
| Link de acesso: |
http://www.repositorio.ufc.br/handle/riufc/18511
|
Resumo: |
This work is a study about the origins of Mathematical Logic and the limits of its applicability to the formal development of Mathematics. Firstly, Dedekind’s arithmetical theory is presented, which was the first theory to provide a precise definition for natural numbers and to demonstrate relying on it all facts commonly known about them. Peano’s axiomatization for Arithmetic is also presented, which in a sense simplified Dedekind’s theory. Then, Frege’s Begriffsschrift is presented, the formal language from which modern Logic originated, and in it are represented Frege’s basic definitions concerning the notion of number. Afterwards, a summary of important topics on the foundations of Mathematics from the first three decades of the twentieth century is presented, beginning with the paradoxes in Set Theory and ending with Hilbert’s formalist doctrine. At last, are presented, in general terms, Gödel’s incompleteness. theorems and Turing’s computability concept, which provided precise answers to the two most important points in Hilbert’s program, to wit, a direct proof of consistency for Arithmetic and the decision problem, respectively. Keywords: 1. Mathematical Logic 2. Foundations of Mathematics 3. Gödel’s incompleteness theorems |
