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Effective Mathematics of the Uncountable by Joel David Hamkins, Denis Hirschfeldt, Noam Greenberg

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SOME RESULTS ON image-COMPUTABLE STRUCTURES

WESLEY CALVERT AND JOHN E. PORTER

§1. Introduction. The theory of effectiveness properties on countable structures whose atomic diagrams are Turing computable is well-studied (see, for instance, [1, 15]). Typical results describe which structures in various classes are computable (or have isomorphic copies that are) [19], or the potential degree of unsolvability of various definable subsets of the structure [16]. The goal of the present paper is to survey some initial results investigating similar concerns on structures which are effective in a different sense.

A rather severe limitation of the Turing model ...

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