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  1. A minimal predicative set theory.Franco Montagna & Antonella Mancini - 1994 - Notre Dame Journal of Formal Logic 35 (2):186-203.
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  • My route to arithmetization.Solomon Feferman - 1997 - Theoria 63 (3):168-181.
    I had the pleasure of renewing my acquaintance with Per Lindström at the meeting of the Seventh Scandinavian Logic Symposium, held in Uppsala in August 1996. There at lunch one day, Per said he had long been curious about the development of some of the ideas in my paper [1960] on the arithmetization of metamathematics. In particular, I had used the construction of a non-standard definition !* of the set of axioms of P (Peano Arithmetic) to show that P + (...)
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  • On the interpretability of arithmetic in set theory.George E. Collins - 1970 - Notre Dame Journal of Formal Logic 11:477.
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  • Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
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  • On the interpretability of arithmetic in set theory.George E. Collins & J. D. Halpern - 1970 - Notre Dame Journal of Formal Logic 11 (4):477-483.
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  • On the untenability of Nelson's predicativism.St Iwan - 2000 - Erkenntnis 53 (1-2):147-154.
    By combining some technical results from metamathematicalinvestigations of systems of Bounded Arithmetic, I will givean argument for the untenability of Nelson 's finitistic program,encapsulated in his book Predicative Arithmetic.
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  • Proof-theoretic analysis by iterated reflection.Lev D. Beklemishev - 2003 - 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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  • Cuts, consistency statements and interpretations.Pavel Pudlák - 1985 - Journal of Symbolic Logic 50 (2):423-441.
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  • On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
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  • Metamathematics of First-Order Arithmetic.Petr Hajek & Pavel Pudlak - 1998 - Springer Verlag.
    People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The (...)
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  • (1 other version)An Inside View of Exp; or, The Closed Fragment of the Provability Logic of $I\Delta0 + \Omega1$ with a Propositional Constant for $\operatorname{Exp}$. [REVIEW]Albert Visser - 1992 - Journal of Symbolic Logic 57 (1):131-165.
    In this paper I give a characterization of the closed fragment of the provability logic of $I \triangle_0 + \mathrm{EXP}$ with a propositional constant for $\mathrm{EXP}$. In three appendices many details on arithmetization are provided.
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  • Predicative arithmetic.Edward Nelson - 1986 - Princeton, N.J.: Princeton University Press.
    This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting (...)
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  • (1 other version)An Inside View of Exp; or, The Closed Fragment of the Provability Logic of IΔ0+ Ω1 with a Propositional Constant for.Albert Visser - 1992 - Journal of Symbolic Logic 57 (1):131-165.
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  • (2 other versions)Review: Edward Nelson, Predicative Arithmetic. [REVIEW]Pavel Pudlak - 1988 - Journal of Symbolic Logic 53 (3):987-989.
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  • A Lattice of Chapters of Mathematics.Jan Mycielski, Pavel Pudlák, Alan S. Stern & American Mathematical Society - 1990 - American Mathematical Society.
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  • Burgess' PV Is Robinson's Q.Mihai Ganea - 2007 - Journal of Symbolic Logic 72 (2):619 - 624.
    In [2] John Burgess describes predicative versions of Frege's logic and poses the problem of finding their exact arithmetical strength. I prove here that PV, the simplest such theory, is equivalent to Robinson's arithmetical theory Q.
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  • (2 other versions)Predicative Arithmetic.Pavel Pudlák - 1988 - Journal of Symbolic Logic 53 (3):987-989.
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  • The formalization of interpretability.Albert Visser - 1991 - Studia Logica 50 (1):81 - 105.
    This paper contains a careful derivation of principles of Interpretability Logic valid in extensions of I0+1.
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