Abstract
We give a precise characterization of parameter free Σ n and II n induction schemata, IΣ n− and I II n− , in terms of reflection principles. This allows us to show that I II n+1− is conservative over IΣ n− w.r.t. boolean combinations of Σ n+1 sentences, for n ≥ 1. In particular, we give a positive answer to a question by R. Kaye, whether the provably recursive functions of I II 2− are exactly the primitive recursive ones.
The research described in this publication was made possible in part by the Russian Foundation for Fundamental Research (project 96-01-01395.
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Beklemishev, L.D. (1997). Parameter free induction and reflection. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1997. Lecture Notes in Computer Science, vol 1289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63385-5_36
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DOI: https://doi.org/10.1007/3-540-63385-5_36
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