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Logic Journal of IGPL Advance Access originally published online on September 24, 2007
Logic Journal of IGPL 2007 15(5-6):433-443; doi:10.1093/jigpal/jzm052
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Large Cardinals and Topology: a Short Retrospective and Some New Results

Samuel G. Da Silva

Departamento de Matemática, Instituto de Matemática, Universidade Federal da Bahia, Campus Ondina, rua Adhemar de Barros s/n, 40170-110, Salvador/Bahia, Brazil. E-mail: samuel{at}ufba.br


  Abstract

This paper is an enlarged version of the short talk delivered at XIV Brazilian Logic Conference (XIV EBL 2006, Itatiaia, Rio de Janeiro). The author's purpose is to present some applications of large cardinals in general topology, pointing out that there are several topological problems that cannot be settled without dealing with inaccessible cardinals. Various "classical examples" are mentioned, together with recent results. In the last section a new result is presented: it is shown that the existence of a separable space with an uncountable closed discrete subset satisfying a certain relative version of countable paracompactness implies the existence of inner models with measurable cardinals.

Key Words: large cardinals • dominating families • relative countable paracompactness • inner models of measurability.

Received for publication 15 October 2006.
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