A Syntactic and Categorical Derivation of G\"{o}del's Completeness Theorem

Hugo Jenkins

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arXiv · 2111.05998

A Syntactic and Categorical Derivation of G\"{o}del's Completeness Theorem

Hugo Jenkins

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Abstract

Considering classical first-order logic with equality, we give a "fully syntactic" construction of the (weak) syntactic category $\text{Syn}(T)$ associated to a consistent theory $T$; we show it is a consistent coherent category; and we show that a morphism of coherent categories $\text{Syn}(T)\to \bf{Set}$ gives rise to a model $\mathcal{M}$ of $T$ in the usual sense. We then invoke Deligne's theorem on small consistent coherent categories.

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BibTeX RIS

Hugo Jenkins. 2021-11-11. A Syntactic and Categorical Derivation of G\"{o}del's Completeness Theorem. https://arxiv.org/abs/2111.05998

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