1. L. D. Beklemishev (2003). Proof-Theoretic Analysis by Iterated Reflection. Archive for Mathematical Logic 42 (6):515-552.
    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 version of the (...)
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  2. L. D. Beklemishev, O. V. Belegradek, K. J. Davey & J. L. Krivine (1994). 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.
     
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  3. L. D. Beklemishev (1991). Provability Logics for Natural Turing Progressions of Arithmetical Theories. Studia Logica 50 (1):107 - 128.
    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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