Structures in Familiar Classes Which Have Scott Rank Ω
نویسندگان
چکیده
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 ω CK 1 + 1. Makkai [12] produced a structure of Scott rank ω CK 1 , which can be made computable [10], and simplified so that it is just a tree [4]. In the present paper, we show that there are further computable structures of Scott rank ω CK 1 in the following classes: undirected graphs, fields of any characteristic, and linear orderings. The new examples share with the Harrison ordering, and the tree in [4], a strong approximability property.
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