An Uncountably Categorical Theory whose Only Computably Presentable Model Is Saturated

by Denis R. Hirschfeldt, Bakhadyr Khoussainov, and Pavel Semukhin

Status: published in the Notre Dame Journal of Formal Logic 47 (2006) 63 - 71.

Availability: journal version and preprint

Abstract. We build an uncountably categorical but not countably categorical theory whose only computably presentable model is the saturated one. As a tool, we introduce a notion related to limitwise monotonic functions.