Let be a given profunctor. We regard it as a category, fully containing both
and
, with additional heteromorphisms
.
Objects of will be regarded as abstract situations (we are given this and that perhaps with certain elementary conditions), objects of
will be called models, and a heteromorphism
is regarded as an interpretation of situation
in model
.
Continue reading “Situation-Tree Logic on a Profunctor”
An abstract infinitary presevervation theorem
We generalize the following results of infinitary first order logic:
A class of models is axiomatizable by universal / existential / positive / negative formulas iff it is closed under submodels / extensions / homomorphic images / surjective homomorphic preimages.
Continue reading “An abstract infinitary presevervation theorem”