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THE SLAMANWEHNER THEOREM IN HIGHER RECURSION THEORY
"... A central concern of computable model theory is the restriction that algebraic structure imposes on the information content of an object of study. One asks about a countable object, what information is coded intrinsically into this object, which cannot be avoided by passing to an isomorphic copy of ..."
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A central concern of computable model theory is the restriction that algebraic structure imposes on the information content of an object of study. One asks about a countable object, what information is coded intrinsically into this object, which cannot be avoided by passing to an isomorphic copy of the object? Given a
SPECTRA OF THEORIES AND STRUCTURES
"... Abstract. 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 viceversa. To this end, we give a ne ..."
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Abstract. 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 viceversa. 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 1random degrees are not degree spectra of structures but are degree spectra of theories. 1.
THE DEGREES OF BIHYPERHYPERIMMUNE SETS
"... Abstract. We study the degrees of bihyperhyperimmune (bihhi) sets. Our main result characterizes these degrees as those that compute a function that is not dominated by any ∆02 function, and equivalently, those that compute a weak 2generic. These characterizations imply that the collection of bi ..."
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Abstract. We study the degrees of bihyperhyperimmune (bihhi) sets. Our main result characterizes these degrees as those that compute a function that is not dominated by any ∆02 function, and equivalently, those that compute a weak 2generic. These characterizations imply that the collection of bihhi Turing degrees is closed upwards. 1.