| 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.) |