# Structures in Familiar Classes Which Have Scott Rank $ω 1^{CK}$ - Mathematics > Logic

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Abstract: There are familiar examples of computable structures having variouscomputable Scott ranks. There are also familiar structures, such as theHarrison ordering, which have Scott rank $\omega 1^{CK}+1$. Makkai produced astructure of Scott rank $\omega 1^{CK}$, which can be made computable, andsimplified so that it is just a tree. In the present paper, we show that thereare further computable structures of Scott rank $\omega 1^{CK}$ in thefollowing classes: undirected graphs, fields of any characteristic, and linearorderings. The new examples share with the Harrison ordering, and the tree justmentioned, a strong approximability property.

Autor: Wesley Calvert, Sergey S. Goncharov, Julia F. Knight

Fuente: https://arxiv.org/