Prime Models of Theories of Computable Linear Orderings

by Denis R. Hirschfeldt

Status: published in the Proceedings of the American Mathematical Society 129 (2001) 3079 - 3083.

Availability: journal version and preprint

Abstract.We answer a long-standing question of Rosenstein by exhibiting a complete theory of linear orderings with both a computable model and a prime model, but no computable prime model. The proof uses the relativized version of the concept of limitwise monotonic function.