Схемы рефлексии и алгебры доказуемости в формальной арифметике@@@Reflection principles and provability algebras in formal arithmetic

[1]  Saul A. Kripke,et al.  Deduction-preserving "Recursive Isomorphisms" between theories , 1967 .

[2]  R. Magari,et al.  Representation and duality theory for diagonalizable algebras , 1975 .

[3]  George Boolos,et al.  Reflection principles and iterated consistency assertions , 1979, Journal of Symbolic Logic.

[4]  K. Gödel.  Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[5]  M. H. Lob,et al.  Solution of a Problem of Leon Henkin , 1955, J. Symb. Log..

[6]  George Boolos,et al.  Omega-consistency and the diamond , 1980 .

[7]  J. Paris,et al.  Accessible Independence Results for Peano Arithmetic , 1982 .

[8]  V. Yu. Shavrukov,et al.  Undecidability in diagonalizable algebras , 1997, Journal of Symbolic Logic.

[9]  Albert Visser,et al.  An Overview of Interpretability Logic , 1997, Advances in Modal Logic.

[10]  Solomon Feferman,et al.  Transfinite recursive progressions of axiomatic theories , 1962, Journal of Symbolic Logic.

[11]  V. Yu. Shavrukov.  A Note on the Diagonalizable Algebras of PA and ZF , 1993, Ann. Pure Appl. Log..

[12]  Lev D. Beklemishev,et al.  Proof-theoretic analysis by iterated reflection , 2003, Arch. Math. Log..

[13]  G. Gentzen.  Die Widerspruchsfreiheit der reinen Zahlentheorie , 1936 .

[14]  Lev D. Beklemishev,et al.  Provability algebras and proof-theoretic ordinals, I , 2001, Ann. Pure Appl. Log..

[15]  S. Feferman.  Arithmetization of metamathematics in a general setting , 1959 .

[16]  Lev D. Beklemishev,et al.  Induction Rules, Reflection Principles, and Provably Recursive Functions , 1995, Ann. Pure Appl. Log..

[17]  Jeremy Avigad,et al.  An Ordinal Analysis of Admissible Set Theory using Recursion on Ordinal Notations , 2002, J. Math. Log..

[18]  J. Barkley Rosser,et al.  Extensions of some theorems of Gödel and Church , 1936, Journal of Symbolic Logic.

[19]  V. Y. Shavrukov.  Isomorphisms of diagonalizable algebras , 1996 .

[20]  Konstantin N. Ignatiev,et al.  On strong provability predicates and the associated modal logics , 1993, Journal of Symbolic Logic.

[21]  Michael Rathjen,et al.  Recent Advances in Ordinal Analysis: Π1 2 — CA and Related Systems , 1995, Bulletin of Symbolic Logic.

[22]  Lev D. Beklemishev.  Notes on local reflection principles , 1995 .

[23]  Lev D. Beklemishev.  Parameter Free Induction and Reflection , 1997, Kurt Gödel Colloquium.

[24]  Shavrukov,et al.  Subalgebras of Diagonalizable Algebras of Theories Containing Arithmetic , 1993 .

[25]  Jeremy Avigad,et al.  The model-theoretic ordinal analysis of theories of predicative strength , 1999, Journal of Symbolic Logic.

[26]  Lawrence J. Pozsgay.  Gödel's Second Theorem for Elementary arithmetic , 1968 .

[27]  Lev D. Beklemishev,et al.  Parameter Free Induction and Provably Total Computable Functions , 1999, Theor. Comput. Sci..

[28]  Ulf R. Schmerl.  A Fine Structure Generated by Reflection Formulas over Primitive Recursive Arithmetic , 1979 .

[29]  Lev D. Beklemishev,et al.  A proof-theoretic analysis of collection , 1998, Arch. Math. Log..

[30]  S. Wainer,et al.  Provably computable functions and the fast growing hierarchy , 1987 .

[31]  Jeremy Avigad,et al.  A Model-Theoretic Approach to Ordinal Analysis , 1997, Bulletin of Symbolic Logic.

[32]  Hiroakira Ono,et al.  Reflection Principles in Fragments of Peano Arithmetic , 1987, Math. Log. Q..

[33]  Domenico Zambella.  Shavrukov's Theorem on the Subalgebras of Diagonalizable Algebras for Theories Containing I Δ0s + exp , 1994, Notre Dame J. Formal Log..

[34]  Lev D. Beklemishev.  Iterated Local Reflection Versus Iterated Consistency , 1995, Ann. Pure Appl. Log..

[35]  Wilhelm Ackermann,et al.  Zur Widerspruchsfreiheit der Zahlentheorie , 1940 .

[36]  W. Pohlers,et al.  A short course in ordinal analysis , 1993 .

[37]  Grigori Mints,et al.  Epsilon-Substitution Method for the Ramified Language and $$\Delta _1^1$$-Comprehension Rule , 1999 .

[38]  Daniel Leivant,et al.  The optimality of induction as an axiomatization of arithmetic , 1983, Journal of Symbolic Logic (JSL).

[39]  D.H.J. de Jongh,et al.  The logic of the provability , 1998 .

[40]  Sergei Tupailo.  Epsilon Substitution Method for Delta11-CR: a Constructive Termination Proof , 2003, Log. J. IGPL.

[41]  Toshiyasu Arai.  Epsilon substitution method for theories of jump hierarchies , 2002, Arch. Math. Log..

[42]  C. Smorynski,et al.  The finite inseparability of the first-order theory of diagonalisable algebras , 1982 .

[43]  Georg Kreisel,et al.  A survey of proof theory , 1968, Journal of Symbolic Logic.

[44]  C. Parsons.  On a Number Theoretic Choice Schema and its Relation to Induction , 1970 .

[45]  R. Statman.  Bounds for proof-search and speed-up in the predicate calculus , 1978 .

[46]  Richard Sommer,et al.  Transfinite Induction within Peano Arithmetic , 1995, Ann. Pure Appl. Log..

[47]  Rohit Parikh,et al.  Existence and feasibility in arithmetic , 1971, Journal of Symbolic Logic.

[48]  Charles D. Parsons,et al.  On n-quantifier induction , 1972, Journal of Symbolic Logic.

[49]  Sergei N. Artëmov,et al.  On propositional quantifiers in provability logic , 1993, Notre Dame J. Formal Log..

[50]  Franco Montagna,et al.  Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic , 1980 .

[51]  Jeff B. Paris,et al.  On the scheme of induction for bounded arithmetic formulas , 1987, Ann. Pure Appl. Log..

[52]  Georg Kreisel,et al.  Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems , 1968 .

[53]  Wilfried Buchholz.  Explaining the Gentzen–Takeuti reduction steps: a second-order system , 2001, Arch. Math. Log..

[54]  Franco Montagna.  On the algebraization of a Feferman's predicate , 1978 .

[55]  J. Barkley Rosser,et al.  Gödel Theorems for Non-Constructive Logics , 1937, Journal of Symbolic Logic.

[56]  Toshiyasu Arai,et al.  Epsilon substitution method for ID1(Pi10 or Sigma10) , 2003, Ann. Pure Appl. Log..

[57]  R. Solovay.  Provability interpretations of modal logic , 1976 .

[58]  W. Pohlers.  Chapter IV – Subsystems of Set Theory and Second Order Number Theory , 1998 .

[59]  Wilfried Buchholz.  Explaining Gentzen's Consistency Proof within Infinitary Proof Theory , 1997, Kurt Gödel Colloquium.