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A well-known polymodal provability logic GLP is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic [9, 5, 8]. This system plays an important role in some recent applications of provabil-ity algebras in proof theory [2, 3]. However, an obstacle in the study of GLP is(More)
Progressions of iterated reflection principles can be used as a tool for ordinal analysis of formal systems. Technically, in some sense, they replace the use of omega-rule. We compare the information obtained by this kind of analysis with the results obtained by the more usual proof-theoretic techniques. In some cases the techniques of iterated reflection(More)
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)