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Master's Dissertation
DOI
Document
Author
Full name
Arthur Francisco Schwerz Cahali
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Mariano, Hugo Luiz (President)
Coniglio, Marcelo Esteban
Lopes, Vinicius Cifú
Title in Portuguese
Lógica de topos e aplicações
Keywords in Portuguese
Lógica categorial
Modelos Heyting-valorados
Topos
Abstract in Portuguese
A primeira noção de topos, a de topos de Grothendieck, surgiu há cerca de 50 anos a partir de uma generalização do conceito de feixe na geometria algébrica. Poucos anos mais tarde, uma axiomatização categorial de algumas das propriedades de um topos de Grothendieck deu origem a uma segunda noção de topos, a de topos elementar; e essa descrição permitiu estabelecer ligações entre essas categorias e teoria dos conjuntos e lógica. Neste trabalho, estudamos a teoria de topos com um foco especial na construção da lógica interna dos topoi, e exploramos sua relação com modelos Heyting-valorados.
Title in English
Topos logic and applications
Keywords in English
Categorical logic
Heyting-valued models
Topos
Abstract in English
The first definition of a topos, that of a Grothendieck topos, emerged roughly 50 years ago from a generalization of the notion of sheaves in algebraic geometry. Few years later, a categorical axiomatization of some properties of Grothendieck topoi gave rise to a second notion of topoi, that of an elementary topos; and this description made it possible to establish connections between these categories and set theory and logic. In this work, we study topos theory with a particular focus on the construction of the internal logic of topoi, and explore its relation to Heyting-valued models.
 
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Publishing Date
2019-07-24
 
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