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

 Title: Soundness and Completeness of an Axiomatic System for First-Order Logic Author: Asta Halkjær From Submission date: 2021-09-24 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. BibTeX: @article{FOL_Axiomatic-AFP, author = {Asta Halkjær From}, title = {Soundness and Completeness of an Axiomatic System for First-Order Logic}, journal = {Archive of Formal Proofs}, month = sep, year = 2021, note = {\url{https://isa-afp.org/entries/FOL_Axiomatic.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.