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.
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