### A Finitely Axiomatized Formalization of Predicate Calculus with Equality

Norman D. Megill
Source: Notre Dame J. Formal Logic Volume 36, Number 3 (1995), 435-453.

#### Abstract

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.

First Page:
Primary Subjects: 03B10
Secondary Subjects: 03B35
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040149359
Mathematical Reviews number (MathSciNet): MR1351416
Digital Object Identifier: doi:10.1305/ndjfl/1040149359
Zentralblatt MATH identifier: 0838.03008

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