24 November 2009

2:30 - 4:00   Trevor Wares (U. Ottawa)
Abstract: I shall sketch a proof that all functions from N^N to itself are continuous in a natural localic topology in the free topos. The proof is based on (unpublished) techniques of Joyal and Fourman on taking sheaves on the glueing of internal locales. The topology in question is related to Brouwer's Bar-Induction. We also sketch some extensions to more general continuity principles.