POSSIBLE m-DIAGRAMS OF MODELS OF ARITHMETIC
نویسنده
چکیده
In this paper we investigate the complexity of m-diagrams of models of various completions of first-order Peano Arithmetic (PA). We obtain characterizations that extend Solovay’s results for open diagrams of models of completions of PA. We first characterize the m-diagrams of models of True Arithmetic by showing that the degrees ofm-diagrams of nonstandard models A of TA are the same for allm ≥ 0. Next, we obtain a more complicated characterization for arbitrary completions of PA. We then provide examples showing that some of the extra complication is needed. Lastly, we characterize sequences of Turing degrees that occur as (deg(T ∩Σn))n∈ω , where T is a completion of PA. §
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