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arXiv · 2310.08374

Rich doctrines and Henkin's Theorem

Francesca Guffanti
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Abstract

We find a possible interpretation of Henkin's Theorem in the language of existential implicational doctrines. Under some smallness assumption, starting from an implicational existential doctrine, with non-trivial fibers, we construct a new doctrine which is rich -- meaning that for every formula $φ(x)$ there is a constant $c$ such that $\exists xφ(x)$ has the same truth-value of $φ(c)$ -- and consistent. To obtain this result, we add a suitable amount of constants and axioms to the starting doctrine. We then show that a rich consistent doctrine admits an appropriate morphism towards the doctrine of subsets -- a model. Henkin's Theorem for doctrines follows from these two results, modeling our proof on the main lines of the original theorem.

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BibTeXRIS

Francesca Guffanti. 2024-07-16. Rich doctrines and Henkin's Theorem. https://arxiv.org/abs/2310.08374

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