Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 37, Number 3 (1996), 452-461.
Classical and Intuitionistic Models of Arithmetic
Given a classical theory T, a Kripke structure is called T-normal (or locally T) if for each , is a classical model of T. It has been known for some time now, thanks to van Dalen, Mulder, Krabbe, and Visser, that Kripke models of HA over finite frames are locally . They also proved that models of over the frame contain infinitely many Peano nodes. We will show that such models are in fact -normal, that is, they consist entirely of Peano nodes. These results are then applied to a somewhat larger class of frames. We close with some general considerations on properties of non-Peano nodes in arbitrary models of .
Notre Dame J. Formal Logic Volume 37, Number 3 (1996), 452-461.
First available in Project Euclid: 14 December 2002
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Wehmeier, Kai F. Classical and Intuitionistic Models of Arithmetic. Notre Dame J. Formal Logic 37 (1996), no. 3, 452--461. doi:10.1305/ndjfl/1039886521. http://projecteuclid.org/euclid.ndjfl/1039886521.