Dear Zinovy, Just a brief note about geometric logic, a positive first-order logic with infinitary disjunctions that is closely related to Grothendieck topos theory. The infinitary disjunctions give one the power to characterize certain infinite domains (including Integer, String, and also finite powerset) up to isomorphism using geometric structure and axioms. I've conjectured that a weaker "arithmetic" logic, with finite disjunctions but an underlying system of type constructors including free algebra constructions, is a good substitute in many situations - I wrote about this in my paper "Locales and toposes as spaces". (The arithmetic logic should be related to Joyal's arithmetic universes much as geometric logic is related to toposes.) I once wrote a paper "Geometric theories and databases", though to be honest I'm not sure a connection with SQL would flow immediately from that paper. Regards, Steve Vickers. Zinovy Diskin wrote:
a good question is what the place of SQL on the scale of logical doctrines is. Since models of SQL-theories include predefined infinite domains with operations (think of Integer and String), and finite domains for tables, model theory for SQL is not classical. I'm not sure but it seems model-theorists call it "metafinite model theory" (Gradel and Gurevich).
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