Π 11 relations and paths through O ∗
نویسندگان
چکیده
When bounds on complexity of some aspect of a structure are preserved under isomorphism, we refer to them as intrinsic. Here, building on work of Soskov [33], [34], we give syntactical conditions necessary and sufficient for a relation to be intrinsically Π1 on a structure. We consider some examples of computable structures A and intrinsically Π1 relations R. We also consider a general family of examples of intrinsically Π1 relations arising in computable structures of maximum Scott rank. For three of the examples, the maximal well-ordered initial segment in a Harrison ordering, the superatomic part of a Harrison Boolean algebra, and the height-possessing part of a Harrison p-group, we show that the Turing degrees
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