Grothendieck's concept of pretopos: its role in algebraic geometry and in logic. Lecture 3.

**Abstract:** "Lecture 1" is meant as the talk I gave at the Grothendieck
meeting recently held at the UdeM. "Lecture 2" is
the one I am giving on March 3rd in this seminar. In Lecture 3, I will
expand the scope of the theme of "pretopos" and
conceptual completeness from finitary logic to infinitary logic. The
main source is still MM/G.E. Reyes: "First order
categorical logic", Springer LNM 611 (1977). The logic is
L-infinity-omega: infinitary propositional connectives,
single-variable quantifiers. The monograph "First order categorical
logic" is about the relating L-infinity-omega to
Grothendieck topos theory. There will be notes posted for all of the lectures.