2:30 - 4:00 M. Makkai (McGill)

Grothendieck's concept of pretopos: its role in algebraic
geometry and in logic
**Abstract:**
In the talk with the same title I gave at the "Hommage à
Grothendieck" meeting on February 19th and 20th, I wrote down two
definitions of "pretopos", the original one given by Grothendieck and
Verdier in SGA4 (1972), and the one given in M.M. & G.E. Reyes, "First
order categorical logic" (1977). In the talk, I will present the
proof, already given in "First order categorical logic", of the
equivalence of the two definitions. Some further comments will be
given on the relations of Grothendieck's sheaf-theoretic approach on
the one hand, and the "direct quantificational" approach on the other
hand, to first-order logic. The talk is purely expository: all results
and proofs (sometimes in slightly different language) already appear
in "First order categorical logic".

## Supplemental notes for the talks in this series