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Abstract: . We establish a course-of-values induction principle for K-finite sets in intuitionistic type theory. Using this principle, we prove a pigeonhole principle conjectured by B'enabou and Loiseau. We also comment on some variants of this pigeonhole principle. 1. Introduction The pigeonhole principle says that a finite set cannot be mapped one-to-one into a proper subset. There is a dual principle saying that a finite set cannot be mapped onto a proper superset. We consider these principles in ... (Update)
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BibTeX entry: (Update)
@article{ blass95induction,
author = "Andreas Blass",
title = "An Induction Principle and Pigeonhole Principles for K-Finite Sets",
journal = "The Journal of Symbolic Logic",
volume = "60",
number = "4",
pages = "1186-1193",
year = "1995",
url = "citeseer.ist.psu.edu/242583.html" }
Citations (may not include all citations):83 Topos Theory (context) - Johnstone - 1977
15 La logique des topos (context) - Boileau, Joyal - 1981
13 Aspects of topoi (context) - Freyd - 1972
6 Handbook of Mathematical Logic (context) - Fourman, of - 1977
4 Oxford Logic Guides (context) - Bell, Local - 1988
2 Toposes without points (context) - Barr - 1974
2 Lecture Notes in Math (context) - Fourman, Scott et al. - 1979
1 Langage interne d'un topos (context) - Coste - 1973
1 Lecture Notes in Math (context) - na-Ortega, Linton et al. - 1979
1 Orbits and monoids in a topos (context) - B'enabou, Loiseau - 1994
1 Some topos-theoretic concepts of finiteness (context) - Kock, Lecouturier et al. - 1975
1 Logical and set-theoretical tools in elementary topoi (context) - Osius - 1975
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