Notre Dame Journal of Formal Logic 37 (3):452-461 (1996)
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Abstract |
Given a classical theory T, a Kripke model K for the language L of T is called T-normal or locally PA just in case the classical L-structure attached to each node of K is a classical model of T. Van Dalen, Mulder, Krabbe, and Visser showed that Kripke models of Heyting Arithmetic (HA) over finite frames are locally PA, and that Kripke models of HA over frames ordered like the natural numbers contain infinitely many PA-nodes. We show that Kripke models of the latter sort are in fact PA-normal. This result is extended to a somewhat larger class of frames.
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Keywords | Heyting Arithmetic Kripke models intuitionistic logic |
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DOI | 10.1305/ndjfl/1039886521 |
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References found in this work BETA
Intuitionistic Validity in T-Normal Kripke Structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
On the Structure of Kripke Models of Heyting Arithmetic.Zoran Marković - 1993 - Mathematical Logic Quarterly 39 (1):531-538.
Finite Kripke Models of HA Are Locally PA.E. C. W. Krabbe - 1986 - Notre Dame Journal of Formal Logic 27:528-532.
Citations of this work BETA
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From Forcing to Satisfaction in Kripke Models of Intuitionistic Predicate Logic.Maryam Abiri, Morteza Moniri & Mostafa Zaare - 2018 - Logic Journal of the IGPL 26 (5):464-474.
Avicenna on Syllogisms Composed of Opposite Premises.Behnam Zolghadr - 2021 - In Mathematics, Logic, and their Philosophies. pp. 433-442.
Intuitionistic Axiomatizations for Bounded Extension Kripke Models.Mohammad Ardeshir, Wim Ruitenburg & Saeed Salehi - 2003 - Annals of Pure and Applied Logic 124 (1-3):267-285.
Every Rooted Narrow Tree Kripke Model of HA is Locally PA.Mohammad Ardeshir & Bardyaa Hesaam - 2002 - Mathematical Logic Quarterly 48 (3):391-395.
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