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Doctoral Thesis
DOI
10.11606/T.45.2012.tde-06092012-214910
Document
Author
Full name
Alberto Marcelino Efigênio Levi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Junqueira, Lucia Renato (President)
Aurichi, Leandro Fiorini
Bianconi, Ricardo
Coniglio, Marcelo Esteban
Passos, Marcelo Dias
Title in Portuguese
Reflexão de funções cardinais
Keywords in Portuguese
funções cardinais
grandes cardinais
Hipótese do Contínuo
Abstract in Portuguese
Neste trabalho investigamos problemas sobre reflexão de funções cardinais, fazendo uso de técnicas como submodelos elementares e Teoria PCF. Mostramos que o grau de Lindelöf reflete todos os cardinais fortemente inacessíveis e que um exemplo de espaço onde a mesma função cardinal não reflita um cardinal fracamente inacessível requer a existência de 0#. Além disso, estendemos um resultado de reflexão do caráter, de espaços Lindelöf para espaços linearmente Lindelöf, obtendo novas equivalências com a Hipótese do Contínuo (CH). Obtivemos ainda várias respostas parciais para problemas clássicos deste tópico de pesquisa.
Title in English
Reflection of cardinal functions
Keywords in English
cardinal functions
Continuum Hypothesis
large cardinals
Abstract in English
This work investigates problems about reflection of cardinal functions, using techniques such as elementary submodels and PCF Theory. We show that the Lindelöf degree reflects all the strongly inaccessible cardinals and that a example of a space in which the same cardinal function does not reflect a weakly inaccessible cardinal requires "0# exists". Furthermore, we extend a result of reflection of the character from Lindelöf spaces to linearly Lindelöf spaces, obtaining new equivalences with the Continuum Hypothesis (CH). We also obtained several partial answers to classic problems of this research topic.
 
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Publishing Date
2012-09-10
 
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