Matthew Harrison-Trainor, Gregory Igusa, Julia F. Knight
Published 2016-06-02Version 1
We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank $\omega_1^{CK}$, the computable infinitary theory is $\aleph_0$-categorical. Millar and Sacks asked whether this was always the case. We answer this question by constructing an example whose computable infinitary theory has non-isomorphic countable models. The standard known computable structures of Scott rank $\omega_1^{CK}+1$ have infinite indiscernible sequences. We give two constructions with no indiscernible ordered triple.
Structures in Familiar Classes Which Have Scott Rank $ω_1^{CK}$
Cohesive Powers of Linear Orders
Scott ranks of models of a theory
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