A Remark on a Peculiarity in the Functor Semantics for Superintuitionistic Predicate Logics with (or without) Equality
نویسنده
چکیده
We notice the following slightly curious (and perhaps, slightly unexpected) logical property of the functor semantics for superintuitionistic predicate logics, contrasting with a well-known property of the usual Kripke semantics. Namely, for a category C its logic (i.e., the logic of all C-sets with the given, fixed C) in general is not reducible to cones (i.e., restrictions of C to upward closed rooted subsets of its frame representation W =Ob(C) ). Related notions and observations are discussed as well.
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