Let be a countable language, let be an isomorphism-type of countable -structures, and let . We say that is -strange if it contains a computable-from- structure and its Scott rank is exactly . For all , -strange structures exist. Theorem (AD): If is a collection of isomorphism-types of countable structures, then for a Turing cone of ’s, no member of is -strange.
"Strange Structures from Computable Model Theory." Notre Dame J. Formal Logic 58 (1) 97 - 105, 2017. https://doi.org/10.1215/00294527-3767941