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 .
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1039886521
Mathematical Reviews number (MathSciNet): MR1434430
Digital Object Identifier: doi:10.1305/ndjfl/1039886521
Zentralblatt MATH identifier: 0871.03027