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Abstract: This paper proves the non-derivability of induction in second order dependent type theory (P 2). This is done by providing a model construction for P 2, based on a saturated sets like interpretation of types as sets of terms of a weakly extensional combinatory algebra. We give countermodels in which the induction principle over natural numbers is not valid. The proof does not depend on the speci c encoding for natural numbers that has been chosen (like e.g. polymorphic Church numerals),... (Update)
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...also for CC , then, in CC , we would have : cpsJMK( z: r(z) which contradicts its consistency. In a recent paper [22], H. Geuvers proved a similar result, namely the non derivability of induction principles in P 2. Despite being close in spirit, the...
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BibTeX entry: (Update)
H. Geuvers. Induction is not derivable in second order dependent type theory. In [1], pp. 166-181. http://citeseer.ist.psu.edu/article/geuvers00induction.html More
@article{ geuvers01induction,
author = "Herman Geuvers",
title = "Induction Is Not Derivable in Second Order Dependent Type Theory",
journal = "Lecture Notes in Computer Science",
volume = "2044",
pages = "166--??",
year = "2001",
url = "citeseer.ist.psu.edu/article/geuvers00induction.html" }
Citations (may not include all citations):266 Information and Computation (context) - Coquand, Huet et al. - 1988
68 Logics and Type systems - Geuvers - 1993
64 Metamathematical investigations of a calculus of constructio.. (context) - Coquand - 1990
20 Tracts in Theoretical Computer Science (context) - Girard, Lafont et al. - 1989
14 Typed lambda calculi (context) - Barendregt - 1992
7 Independence of the induction principle and the axiom of cho.. (context) - Streicher - 1991
2 Constructive Natural Deduction and its \Modest (context) - Longo, Moggi - 1988
1 Extending models of second order logic to models of second o.. (context) - Geuvers - 1996
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