Structures in Familiar Classes Which Have Scott Rank $\omega_1^{CK}$
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Publication:6208858
arXiv0803.3296MaRDI QIDQ6208858
Wesley Calvert, J. F. Knight, S. S. Goncharov
Publication date: 22 March 2008
Abstract: There 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 . Makkai produced a structure of Scott rank , 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 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.
Computable structure theory, computable model theory (03C57) Theory of numerations, effectively presented structures (03D45)
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