J Austral Math Soc Ser A 46 pp343--355, 1989.

Homogenous Models and Almost Decidability

Terry Millar

Abstract

Countable homogenous models are 'simple' objects from a model theoretic point of view. From a recursion theoretic point of view they can be complex. For instance the elementary theory of such a model might be undecidable, or the set of complete types might be recursively complex. Unfortunately even if neither of these conditions holds, such a model still can be undecidable. This paper investigates countable homogenous models with respect to a weaker notion of decidability called almost decidable. It is shown that for theoreies that have only countably many type spectra, and countable homogenous model of such a theory that has a S₂ type spectrum is almost decidable.

1980 AMS Subject Classification (1985 Revision): 03C57

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Authors

Terry Millar

Department of Mathematics, University of Wisconsin, Madison, Misconsin 53706, U.S.A.