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.