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EFFECTIVELY NOWHERE SIMPLE RELATIONS ON COMPUTABLE STRUCTURES

Let A be a computable structure and let R be an additional relation on its domain. The notion of “quasi-simplicity” of R on A, first studied by G. Hird, is analogous to the computabilitytheoretic notion of simplicity, given the definability of various subrelations of ¬R. In the present paper, we define corresponding versions of the notions “nowhere simple” and “effectively nowhere simple.” We establish a sufficient condition for existence of noncomputable effectively nowhere simple relations on a restricted class of computable structures.