Geodesic
Constructing Kripke Models of Certain Fragments of Heyting's Arithmetic
Publications de l'Institut Mathématique, _N_S_63 (1998) no. 77, p. 1 .

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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 Smorynski's collection operation introduced in [S73].
Classification : 03F50 03F55 
@article{PIM_1998_N_S_63_77_a0,
     author = {Kai F. Wehmeier},
     title = {Constructing {Kripke} {Models} of {Certain} {Fragments} of {Heyting's} {Arithmetic}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {1 },
     publisher = {mathdoc},
     volume = {_N_S_63},
     number = {77},
     year = {1998},
     zbl = {0946.03070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1998_N_S_63_77_a0/}
}
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Kai F. Wehmeier. Constructing Kripke Models of Certain Fragments of Heyting's Arithmetic. Publications de l'Institut Mathématique, _N_S_63 (1998) no. 77, p. 1 . http://geodesic.mathdoc.fr/item/PIM_1998_N_S_63_77_a0/