Strongly minimal theories with recursive models

  • Uri Andrews

    University of Wisconsin, Madison, USA
  • Julia F. Knight

    University of Notre Dame, USA

Abstract

We give effectiveness conditions on a strongly minimal theory guaranteeing that all countable models have computable copies. In particular, we show that if is strongly minimal and for all , is , uniformly in , then every countable model has a computable copy. A longstanding question of computable model theory asked whether for a strongly minimal theory with one computable model, every countable model has an arithmetical copy. Relativizing our main result, we get the fact that if there is one computable model, then every countable model has a copy.

Cite this article

Uri Andrews, Julia F. Knight, Strongly minimal theories with recursive models. J. Eur. Math. Soc. 20 (2018), no. 7, pp. 1561–1594

DOI 10.4171/JEMS/793