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On recursion theory in $$I\Sigma_ 1$$. (English) Zbl 0703.03019
In 1986, the second author showed a priority-free proof of the existence of an intermediate r.e. degree [Lect. Notes Comput. Sci. 233, 493-500 (1986; Zbl 0615.03033)]. In the present paper, the authors discuss the problem of whether Kučera’s priority-free proof formalizes in the fragment of first order arithmetic $$I\Sigma_ 1$$ (the basic theory $$PA^-$$ plus induction for $$\Sigma_ 1$$ formulas). It is shown that the low basis theorem is meaningful and provable in $$I\Sigma_ 1$$ and that the priority-free solution to Post’s problem formalizes in this theory.
Reviewer: Li Xiang

##### MSC:
 03D25 Recursively (computably) enumerable sets and degrees 03F30 First-order arithmetic and fragments
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##### References:
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