Toposes as models of Set Theory
speaker: Peter Johnstone (University of Cambridge)abstract: As viewed "from the outside", a topos is a generalized space, but from its own "internal" point of view it is a truism that "every topos thinks it is the category of sets", albeit in a non-classical universe where the law of excluded middle may not hold. Thirty years ago, Fourman gave a concrete expression to this truism, by constructing an interpretation of intuitionistic ZF set theory in an arbitrary Grothendieck topos, but the construction is still not well understood. In this lecture we shall give a simple presentation of it, and then show how it may be used, in conjunction with the notion of classifying topos, to give topos-theoretic versions of independence proofs for such things as the Continuum Hypothesis and Suslin's Hypothesis. Freyd has also shown that it can be used to prove the independence of the Axiom of Choice; we describe his models, and discuss how they relate to classifying toposes
timetable:
Wed 28 Apr, 14:30 - 16:30, Aula Dini
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