Abstract
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.
Citation
Bakhadyr Khoussainov. Andre Nies. Richard A. Shore. "Computable Models of Theories with Few Models." Notre Dame J. Formal Logic 38 (2) 165 - 178, Spring 1997. https://doi.org/10.1305/ndjfl/1039724885
Information