Logic – Profunctors

July 2, 2010

Situation-Tree Logic on a Profunctor

Let $\ct F:\ct S\ag\ct M$ be a given profunctor. We regard it as a category, fully containing both $\ct S$ and $\ct M$ , with additional heteromorphisms $S\to M$ .
Objects of $\ct S$ will be regarded as abstract situations (we are given this and that perhaps with certain elementary conditions), objects of $\ct M$ will be called models, and a heteromorphism $S\to M$ is regarded as an interpretation of situation $S$ in model $M$ .
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June 23, 2010November 30, 2023

An abstract infinitary presevervation theorem

We generalize the following results of infinitary first order logic:
A class $\C K$ of models is axiomatizable by universal / existential / positive / negative formulas iff it is closed under submodels / extensions / homomorphic images / surjective homomorphic preimages.

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