Notre Dame Journal of Formal Logic

Basic Predicate Calculus

Wim Ruitenburg


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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Notre Dame J. Formal Logic, Volume 39, Number 1 (1998), 18-46.

First available in Project Euclid: 7 December 2002

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Zentralblatt MATH identifier

Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03C90: Nonclassical models (Boolean-valued, sheaf, etc.) 03D35: Undecidability and degrees of sets of sentences 03F30: First-order arithmetic and fragments


Ruitenburg, Wim. Basic Predicate Calculus. Notre Dame J. Formal Logic 39 (1998), no. 1, 18--46. doi:10.1305/ndjfl/1039293019.

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