We build an א₁-categorical but not א₀-categorical theory whose only computably presentable model is the saturated one. As a tool, we introduce a notion related to limitwise monotonic functions.
"An Uncountably Categorical Theory Whose Only Computably Presentable Model Is Saturated." Notre Dame J. Formal Logic 47 (1) 63 - 71, 2006. https://doi.org/10.1305/ndjfl/1143468311