Lev D. Beklemishev

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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 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 provability algebras in proof theory [2, 3]. However, an obstacle in the study of GLP is(More)
We study an extension of Japaridze’s polymodal logic GLP with transfinitely many modalities and develop a provability-algebraic ordinal notation system up to the ordinal Γ0. In the papers [1, 2] a new algebraic approach to the traditional prooftheoretic ordinal analysis was presented based on the concept of graded provability algebra. The graded provability(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 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)
A well known result of D Leivant states that over basic Kalmar ele mentary arithmetic EA the induction schema for n formulas is equivalent to the uniform re ection principle for n formulas We show that frag ments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of re ection principles as well Thus the(More)
We present a simplified proof of Japaridze’s arithmetical completeness theorem for the well-known polymodal provability logic GLP. The simplification is achieved by employing a fragment J of GLP that enjoys a more convenient Kripke-style semantics than the logic considered in the papers by Ignatiev and Boolos. In particular, this allows us to simplify the(More)
We give a precise characterization of parameter free n and n induction schemata I n and I n in terms of re ection principles This allows us to show that I n is conservative over I n w r t boolean combinations of n sentences for n In particular we give a positive answer to a question by R Kaye whether the provably recursive functions of I are exactly the(More)