Structures in Familiar Classes Which Have Scott Rank Ω


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… (More)