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14On Topological Models of GLPIn Ralf Schindler (ed.), Ways of Proof Theory, De Gruyter. pp. 135-156. 2010.
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23On the limit existence principles in elementary arithmetic and Σ n 0 -consequences of theoriesAnnals of Pure and Applied Logic 136 (1-2): 56-74. 2005.We study the arithmetical schema asserting that every eventually decreasing elementary recursive function has a limit. Some other related principles are also formulated. We establish their relationship with restricted parameter-free induction schemata. We also prove that the same principle, formulated as an inference rule, provides an axiomatization of the Σ2-consequences of IΣ1.Using these results we show that ILM is the logic of Π1-conservativity of any reasonable extension of parameter-free Π…Read more
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45Franco Montagna’s Work on Provability Logic and Many-valued LogicStudia Logica 104 (1): 1-46. 2016.Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic
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31Reflection algebras and conservation results for theories of iterated truthAnnals of Pure and Applied Logic 173 (5): 103093. 2022.
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5Calibrating Provability Logic: From Modal Logic to Reflection CalculusIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 89-94. 1998.
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20Dick de Jongh and Franco Montagna. Provable fixed points. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 34 , pp. 229–250 (review)Journal of Symbolic Logic 58 (2): 715-717. 1993.
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17Smullyan Raymond M.. Diagonalization and self-reference. Oxford logic guides, no. 27. Clarendon Press, Oxford University Press, Oxford and New York1994, xv + 396 pp (review)Journal of Symbolic Logic 61 (3): 1052-1055. 1996.
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25Wolfgang Burr. Fragments of Heyting arithmetic. The journal of symbolic logic, vol. 65 , pp. 1223–1240 (review)Bulletin of Symbolic Logic 8 (4): 533-534. 2002.
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4A Note on Strictly Positive Logics and Word Rewriting SystemsIn Sergei Odintsov (ed.), Larisa Maksimova on Implication, Interpolation, and Definability, Springer Verlag. 2018.We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable finitely axiomatizable strictly positive normal modal logics. The translation has its counterpart on the level of proofs: we formulate a natural deep inference proof system for strictly positive logics generalizing derivations in word rewriting systems. We also make some obse…Read more
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28A many-sorted variant of Japaridze’s polymodal provability logicLogic Journal of the IGPL 26 (5): 505-538. 2018.
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Leloup, G., Rings of monoids elementarily equivalent to polynomial rings Miller, C., Expansions of the real field with power functions Ozawa, M., Forcing in nonstandard analysis Rathjen, M., Proof theory of reflection (review)Annals of Pure and Applied Logic 68 343. 1994.
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13Calibrating Provability Logic: From Modal Logic to Reflection CalculusIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 89-94. 1998.
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24Provability, complexity, grammarsAmerican Mathematical Society. 1999.(2) Vol., Classification of Propositional Provability Logics LD Beklemishev Introduction Overview. The idea of an axiomatic approach to the study of ...
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53Provability logics for natural Turing progressions of arithmetical theoriesStudia Logica 50 (1). 1991.Provability logics with many modal operators for progressions of theories obtained by iterating their consistency statements are introduced. The corresponding arithmetical completeness theorem is proved
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212002 european summer meeting of the association for symbolic logic logic colloquium'02Bulletin of Symbolic Logic 9 (1): 71. 2003.
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1918th workshop on logic, language, information and computation (wollic 2011)Bulletin of Symbolic Logic 18 (1): 152-153. 2012.
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46Proof-theoretic analysis by iterated reflectionArchive for Mathematical Logic 42 (6): 515-552. 2003.Progressions of iterated reflection principles can be used as a tool for the ordinal analysis of formal systems. We discuss various notions of proof-theoretic ordinals and compare the information obtained by means of the reflection principles with the results obtained by the more usual proof-theoretic techniques. In some cases we obtain sharper results, e.g., we define proof-theoretic ordinals relevant to logical complexity Π1 0 and, similarly, for any class Π n 0 . We provide a more general ver…Read more
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39On bimodal logics of provabilityAnnals of Pure and Applied Logic 68 (2): 115-159. 1994.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 . Carlson characterized the provability logic for essentially reflexive extensions of theories, i.e. for pairs similar to . Here we study pairs of theories such that the gap between and is not so wide. In view of some general results concerning the problem of classification of the bimodal provability logics we are particu…Read more
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23Inexhaustibility: a non-exhaustive treatment and a survey on transfinite progressions (review)Bulletin of Symbolic Logic 14 (2): 258-259. 2008.
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69On propositional quantifiers in provability logicNotre Dame Journal of Formal Logic 34 (3): 401-419. 1993.
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33Review: Raymond M. Smullyan, Diagonalization and Self-Reference (review)Journal of Symbolic Logic 61 (3): 1052-1055. 1996.
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35On the complexity of arithmetical interpretations of modal formulaeArchive for Mathematical Logic 32 (3): 229-238. 1993.
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21Leo Corry, David Hilbert and the axiomatization of physics (1998–1918), Springer, Netherlands (2004) ISBN 1-4020-2777-X (513 pp., Euro 160, US$ 179, £111, Hardcover) (review)Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (2): 388-390. 2006.