Intuitionistic Open Induction and Least Number Principle and the Buss Operator

Notre Dame Journal of Formal Logic 39 (2):212-220 (1998)
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In "Intuitionistic validity in -normal Kripke structures," Buss asked whether every intuitionistic theory is, for some classical theory , that of all -normal Kripke structures for which he gave an r.e. axiomatization. In the language of arithmetic and denote PA plus Open Induction or Open LNP, and are their intuitionistic deductive closures. We show is recursively axiomatizable and , while . If proves PEM but not totality of a classically provably total Diophantine function of , then and so . A result due to Wehmeier then implies . We prove is not -conservative over . If , then is not closed under MR or Friedman's translation, so range (). Both and are closed under the negative translation



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Weak Arithmetics and Kripke Models.Morteza Moniri - 2002 - Mathematical Logic Quarterly 48 (1):157-160.

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References found in this work

Fragments of $HA$ based on $\Sigma_1$ -induction.Kai F. Wehmeier - 1997 - Archive for Mathematical Logic 37 (1):37-49.
Intuitionistic validity in T-normal Kripke structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
Finite Kripke models of HA are locally PA.E. C. W. Krabbe - 1986 - Notre Dame Journal of Formal Logic 27:528-532.
On the structure of kripke models of heyting arithmetic.Zoran Marković - 1993 - Mathematical Logic Quarterly 39 (1):531-538.

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