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Summer 1995 A Finitely Axiomatized Formalization of Predicate Calculus with Equality
Norman D. Megill
Notre Dame J. Formal Logic 36(3): 435-453 (Summer 1995). DOI: 10.1305/ndjfl/1040149359


We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of Meredith. The usual primitive notions of free variable and proper substitution are absent, making it easy to verify proofs in a machine-oriented application. Completeness results are presented. The example of Zermelo-Fraenkel set theory is shown to be finitely axiomatized under the formalization. The relationship with resolution-based theorem provers is briefly discussed. A closely related axiomatization of traditional predicate calculus is shown to be complete in a strong metamathematical sense.


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Norman D. Megill. "A Finitely Axiomatized Formalization of Predicate Calculus with Equality." Notre Dame J. Formal Logic 36 (3) 435 - 453, Summer 1995.


Published: Summer 1995
First available in Project Euclid: 17 December 2002

zbMATH: 0838.03008
MathSciNet: MR1351416
Digital Object Identifier: 10.1305/ndjfl/1040149359

Primary: 03B10
Secondary: 03B35

Rights: Copyright © 1995 University of Notre Dame

Vol.36 • No. 3 • Summer 1995
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