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Master's Dissertation
DOI
Document
Author
Full name
Guilherme Trajano de Santana
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Dias, Rodrigo Roque (President)
Aurichi, Leandro Fiorini
Boero, Ana Carolina
Title in Portuguese
Conjuntos fortemente nulos e fortemente magros
Keywords in Portuguese
Conjectura de Borel
Conjectura dual de Borel
Conjuntos fortemente magros
Conjuntos fortemente nulos
Dualidade
Abstract in Portuguese
O presente trabalho tem como objetivo apresentar os conjuntos fortemente nulos e fortemente magros. Mais especicamente, iremos apresentar algumas aplicações e avaliar a independência de ZFC de armações envolvendo tais conjuntos. Com relação às aplicações, daremos alguns exemplos de conjuntos fortemente nulos e fortemente magros, estudaremos a aditividade do ideal formado pelos subconjuntos fortemente nulos da reta real, apresentaremos uma análise da relação entre a propriedade fortemente nulo e translações de subconjuntos da reta, mostraremos equivalências da Conjectura de Borel em espaços métricos, com a armação R-BC e com uma armação envolvendo jogos. Com relação a análise de independência de armações de ZFC, mostraremos que a Conjectura Dual de Borel é independente de ZFC e que a negação da Conjectura de Borel é consistente com ZFC.
Title in English
Strongly null and strongly meager sets
Keywords in English
Borel conjecture
Dual Borel conjecture
Duality
Strongly meager
Strongly null
Abstract in English
The present work aims to present the strongly null and strongly meager sets. More specically, we will present some applications and evaluate the independence of ZFC from statements involving such sets. With respect to the applications, we will give some examples of strongly null and strongly meager sets, we will study the additivity of the ideal formed by the strongly null subsets of the real line, we will present an analysis of the relation between the strongly null property and the subsets of the line, of the Borel Conjecture in metric spaces, with the statement R-BC and with a statement involving games. Regarding the analysis of the independence of ZFC statements, we will show that the Borel Dual Conjecture is independent of ZFC and that the negation of the Borel Conjecture is consistent with ZFC.
 
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Publishing Date
2019-09-26
 
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