Spectra of Theories and Structures
نویسندگان
چکیده
We introduce the notion of a degree spectrum of a complete theory to be the set of Turing degrees that contain a copy of some model of the theory. We generate examples showing that not all degree spectra of theories are degree spectra of structures and vice-versa. To this end, we give a new necessary condition on the degree spectrum of a structure, specifically showing that the set of PA degrees and the upward closure of the set of 1-random degrees are not degree spectra of structures but are degree spectra of theories.
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