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\title{Soundness and Completeness of an Axiomatic System for First-Order Logic}
\author{Asta Halkjær From}
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\begin{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)~\cite{Smullyan1968}.
  The completeness proof is in the Henkin style~\cite{Henkin96} 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.
\end{abstract}

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