EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 63 (77), pp. 1--8 (1998)

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Constructing Kripke models of certain fragments of Heyting's arithmetic

Kai F. Wehmeier

Institut für Mathematische Logik und Grundlagenforschung, Münster, Germany

Abstract: We present nontrivial methods of constructing Kripke models for the fragments of HA obtained by restricting the induction schema to instances with ${\varPi}_1$- and ${\varPi}_2$-induction formulae respectively. The model construction for ${\varPi}_1$-induction was applied in [W96a] and [W97] to investigate the provably recursive functions of this theory. The construction of ${\varPi}_2$-induction models is a modification of Smory\'nski's collection operation introduced in [S73].

Classification (MSC2000): 03F50; 03F55

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Electronic fulltext finalized on: 6 Apr 2000. This page was last modified: 16 Nov 2001.

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