Mathematical logic seminar - October 16, 2007

Time: 12:00 - 13:20

Room: Scaife Hall 219

Speaker:     Peter Lumsdaine   
Department of Mathematical Sciences
Carnegie Mellon University

Title: Sheaves II: Logic in sheaves on a space

Abstract: I will generalise the previous lecture to sheaves on a Grothendieck site, show (some of) how first- and higher-order logic is modelled in a category of sheaves, and use this to present an independence result: there is a category of sheaves on a space in which there is a Cauchy sequence of rationals with no modulus of convergence. Thus, such a sequence is consistent with higher-order Heyting arithmetic. (This result is due in a stronger form to Lubarsky.)