Abstract
We establish a completeness theorem for first-order basic predicate logic BQC, a proper subsystem of intuitionistic predicate logic IQC, using Kripke models with transitive underlying frames. We develop the notion of functional well-formed theory as the right notion of theory over BQC for which strong completeness theorems are possible. We also derive the undecidability of basic arithmetic, the basic logic equivalent of intuitionistic Heyting Arithmetic and classical Peano Arithmetic
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DOI 10.1305/ndjfl/1039293019
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References found in this work BETA

Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Basic Propositional Calculus I.Mohamed Ardeshir & Wim Ruitenberg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.

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Citations of this work BETA

The de Jongh Property for Basic Arithmetic.Mohammad Ardeshir & S. Mojtaba Mojtahedi - 2014 - Archive for Mathematical Logic 53 (7-8):881-895.
Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.

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