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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 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)

Gurevich and Neeman introduced Distributed Knowledge Authorization Language (DKAL). The world of DKAL consists of communicating principals computing their own knowledge in their own states. DKAL is based on a new logic of information, the so-called infon logic, and its efficient subsystem called primal logic. In this paper we simplify Kripkean semantics of… (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 investigate the bimodal logics sound and complete under the interpretation of modal operators as the provability predicates in certain natural pairs of arithmetical theories (F', ?2). Carlson characterized the provability logic for essentially reflexive extensions of theories, i.e. for pairs similar to (PA, ZF). Here we study pairs of theories (F', %!)… (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)