Homogeneous models and decidability
Terrence S. Millar · Pacific Journal of Mathematics · 1980
Fix a countable first order structure 3f realizing only recursive types.It is known that if sf 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 Sf that are homogeneous.This paper provides a negative answer to that conjecture.