Some new computable structures of high rank

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-07, Vol.146 (7), p.3097-3109
Main Authors: HARRISON-TRAINOR, MATTHEW, IGUSA, GREGORY, KNIGHT, JULIA F.
Format: Article
Language:English
Subjects:
E. LOGIC AND FOUNDATIONS
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13967