Noetherianity in a class of first-order theories
نویسنده
چکیده
We call a theory a Dedekind theory if every complete quantifier-free type with one free variable either has a trivial positive part or it is isolated by a positive quantifier-free formula. The theory of vector spaces and the theory fields are examples. We prove that in a Dedekind theory all positive quantifier-free types are principal so, in a sense, Dedekind theories are Noetherian. We show that saturated existentially closed models of Dedekind theories, if not countably categorical, are Zariski geometries.
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