Complexity of model-theoretic notions.
Russell W. Myers · Notre Dame Journal of Formal Logic · 1980
The main result of this paper is that if T is a countable theory and F a type, then the predicate 'T has a model omitting F" is sharply Z} in the sense of recursion theory, and particularly that every S} predicate is recursive in this predicate.We will also show that the predicate "T is coo-categorical" is arithmetical.