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)