M. Coste, Langage interne d'un topos, S'eminaire B'enabou, Universit'e Paris-Nord, 1973.  Home/Search   Document Not in Database   Summary   Related Articles

....pigeonhole principle proved constructively by B enabou and Loiseau, who noted that their argument does not establish a natural stronger version of the principle. Throughout this paper we work in an intuitionistic type theory of the sort that arises as the internal logic of an elementary topos [3, 5, 6, 7, 8, 10, 12]. Although the questions we consider originated in the course of topos theoretic work of B enabou and Loiseau [4] many of our results are theorems of intuitionistic type theory (in fact of intuitionistic third order logic) and involve no reference to topoi. Of the several concepts of finiteness ....

....principle, showing that a weak version is intuitionistically provable but a strong version is not. The final Section 6 is about some variants of the dual pigeonhole principle. 2. Preliminaries The set theory and logic used in this paper are an intuitionistic type theory of the sort described in [3, 5, 6, 7, 8, 10, 12]. These references differ in some details, but the differences will not matter in our work. We shall work with elements, subsets, and families of subsets of some fixed but arbitrary type U , as well as (partial) functions from U to U . A set is called inhabited if there exists an element in it. ....

M. Coste, Langage interne d'un topos, S'eminaire B'enabou, Universit'e Paris-Nord, 1973.

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