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May 27, 2010 at 18:18 comment added Todd Trimble Thanks for bringing this to my attention, Francois. I may have something to add a little later.
May 27, 2010 at 17:55 comment added François G. Dorais Todd, you might want to check out this old question of Joel David Hamkins - mathoverflow.net/questions/11261/… - My answer there overlaps with yours, but you probably could add your two cents.
May 27, 2010 at 13:30 comment added Todd Trimble I'm going on memory here, but I may have picked up on the ideas in the first paragraph by reading the first few chapters of Handbook of Mathematical Logic. Johnstone's book is also really good, and goes into a lot of detail. We're adding bits and pieces to the nLab (e.g., stuff surrounding "ultrafilter theorem"). As for the stuff in the last paragraph, you probably have Mac Lane-Moerdijk as a reference; the stuff from Lawvere comes from his Chicago lecture notes Variable Sets, Etendu, and Variable Structures in Topoi. Sorry I don't have more!
May 27, 2010 at 13:23 comment added Steven Gubkin Mac Lane and Moerdijk's book "Sheaves in Geometry and Logic" spells out the connections very nicely.
May 27, 2010 at 13:10 comment added David Carchedi Wow, that's really cool! Thanks! Is there anywhere I can read more about this?
May 27, 2010 at 13:03 history answered Todd Trimble CC BY-SA 2.5