Homogeneous models and decidability

Terrence Millar

Vol. 91 (1980), No. 2, 407–418

DOI: 10.2140/pjm.1980.91.407

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