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Winter 1998 Basic Predicate Calculus
Wim Ruitenburg
Notre Dame J. Formal Logic 39(1): 18-46 (Winter 1998). DOI: 10.1305/ndjfl/1039293019

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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Wim Ruitenburg. "Basic Predicate Calculus." Notre Dame J. Formal Logic 39 (1) 18 - 46, Winter 1998. https://doi.org/10.1305/ndjfl/1039293019

Information

Published: Winter 1998
First available in Project Euclid: 7 December 2002

zbMATH: 0967.03005
MathSciNet: MR1671797
Digital Object Identifier: 10.1305/ndjfl/1039293019

Subjects:
Primary: 03B20
Secondary: 03C90, 03D35, 03F30

Rights: Copyright © 1998 University of Notre Dame

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Vol.39 • No. 1 • Winter 1998
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