Characterization of the Axiomatizable Prenex Fragments of First-Order Gödel Logics
نویسندگان
چکیده
The prenex fragments of first-order infinite-valued Gödel logics are classified. It is shown that the prenex Gödel logics characterized by finite and by uncountable subsets of [0,1] are axiomatizable, and that the prenex fragments of all countably infinite Gödel logics are not axiomatizable.
منابع مشابه
First-order Gödel logics
First-order Gödel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V ). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V , or eve...
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