Lev D. Beklemishev

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We study a propositional polymodal provability logic GLP introduced by G. Japaridze. The previous treatments of this logic, due to Japaridze and Ignatiev (see [11, 7]), heavily relied on some non-finitary principles such as transfinite induction up to ε0 or reflection principles. In fact, the closed fragment of GLP gives rise to a natural system of ordinal(More)
A well-known result of D. Leivant states that, over basic Kalmar elementary arithmetic EA , the induction schema for n formulas is equivalent to the uniform reeection principle for n+1 formulas. We show that fragments of arithmetic axiomatized by v arious forms of induction rules admit a precise axiomatization in terms of reeection principles as well. Thus,(More)
We study the classes of computable functions that can be proved to be total by means of parameter free C, and 4 induction schemata, ZC; and ZlI;, over Kalmar elementary arithmetic. We give a positive answer to a question, whether the provably total computable functions of Zq are exactly the primitive recursive ones, and show that the class of such functions(More)