Computable Models of Theories with Few Models
Bakhadyr Khoussainov, André Nies, Richard A. Shore · Notre Dame Journal of Formal Logic · 1997
In this paper we investigate computable models of $\aleph_1$-categorical theories and Ehrenfeucht theories. For instance, we give an example of an $\aleph_1$-categorical but not $\aleph_0$-categorical theory $T$ such that all the countable models of $T$ except its prime model have computable presentations. We also show that there exists an $\aleph_1$-categorical but not $\aleph_0$-categorical theory $T$ such that all the countable models of $T$ except the saturated model, have computable presentations.