Soundness and Completeness of an Axiomatic System for First-Order Logic

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Abstract

This work is a formalization of the soundness and completeness of an axiomatic system for first-order logic. The proof system is based on System Q1 by Smullyan and the completeness proof follows his textbook "First-Order Logic" (Springer-Verlag 1968). The completeness proof is in the Henkin style where a consistent set is extended to a maximal consistent set using Lindenbaum's construction and Henkin witnesses are added during the construction to ensure saturation as well. The resulting set is a Hintikka set which, by the model existence theorem, is satisfiable in the Herbrand universe.
Original languageEnglish
Book seriesArchive of Formal Proofs
Volume2021
Number of pages19
ISSN2150-914X
Publication statusPublished - 2021

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