Sobre a Consistência da Hipótese do Contínuo

• Autor(a) principal: CARDOSO, Matheus Pires
• Data de Publicação: 2023
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UFT
• Texto Completo: http://hdl.handle.net/11612/4795
• topic: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Teoria dos Conjuntos; Ordinais; Cardinais; Números Transfinitos; Construíeis; Hipótese do Contínuo; Set Theory; Ordinals; Cardinals; Transfinite Numbers; Construtible; Continuum Hypothesis

First formulated by Georg Cantor(1845-1918), the Continuum Hypothesis remained almost a century without a solution being given, a conjecture became as intriguing as the paradoxes that appeared in the set theory that David Hilbert, in 1900, inserted as the first problem on his fa- mous list, he had tried unsuccessfully to prove it, but it was with the solution of another problem on the list that a glimpse of proof of this conjecture began to form. In 1930, Kurt Godel after ̈ solving one of the problems in the list and having discovered two important theorems for logic also brought proof of the consistency of the Continuous Hypothesis. It is this proof that this work will make explicit, starting with the development of the axiomatic theory of the sets and later working with a model of the Zermelo-Fraenkel (ZF) system so that conquered that if ZF added the Continuum Hypothesis produce in a contradiction we can then produce a contradic- tion in ZF.