Vol. 91, No. 2, 1980

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Homogeneous models and decidability

Terrence Millar

Vol. 91 (1980), No. 2, 407–418
Abstract

Fix a countable first order structure 𝒜 realizing only recursive types. It is known that if 𝒜 is prime or saturated then it is decidable iff the set of types it realizes is recursively enumerable. A natural conjecture was that the techniques of proof for those two cases could be combined to produce the result for those 𝒜 that are homogeneous. This paper provides a negative answer to that conjecture.

Mathematical Subject Classification 2000
Primary: 03C50
Secondary: 03C57
Milestones
Received: 22 May 1978
Published: 1 December 1980
Authors
Terrence Millar