Structures in Familiar Classes Which Have Scott Rank $ω_1^{CK}$

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dc.creatorCalvert, Wesley
dc.creatorGoncharov, Sergey S.
dc.creatorKnight, Julia F.
dc.date2008-03-22
dc.date.accessioned2026-07-07T09:28:02Z
dc.date.available2026-07-07T09:28:02Z
dc.descriptionThere are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank $ω_1^{CK}+1$. Makkai produced a structure of Scott rank $ω_1^{CK}$, which can be made computable, and simplified so that it is just a tree. In the present paper, we show that there are further computable structures of Scott rank $ω_1^{CK}$ in the following classes: undirected graphs, fields of any characteristic, and linear orderings. The new examples share with the Harrison ordering, and the tree just mentioned, a strong approximability property.
dc.descriptionAdvances in Logic (Proceedings of the North Texas Logic Conference, October 8--10, 2004), Contemporary Mathematics 425 (2007), American Mathematical Society, 49--66
dc.identifierhttps://arxiv.org/abs/0803.3296
dc.identifierhttp://arxiv.org/abs/0803.3296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157315
dc.subjectLogic
dc.subject03D45; 03C57
dc.titleStructures in Familiar Classes Which Have Scott Rank $ω_1^{CK}$
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