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Statement of problems and results In this paper we investigate and solve the problem classifying the Turing complexity of stable models of finite and recursive predicate logic programs. Gelfond-Lifschitz  introduced the concept of a stable model M of a Predicate Logic Program P . Here we show that, up to a recursive 1-1 coding, the set of all stable models of finite Predicate Logic Programs and the Π 0 1 classes (equivalently, the set of all infinite branches of recursive trees) coincidedoi:10.1016/s0743-1066(14)80008-3 fatcat:ukrtmiky6ngvnasnonojeox4ye