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On local proof restrictions for strong theories

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Rozprawy Matematyczne tom/nr w serii: 108 wydano: 1973
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CONTENTS
Introduction.................................................................................................................... 5
Chapter 1. Preliminaries............................................................................................. 7
Chapter 2. Formal arithmetization............................................................................. 12
Chapter 3. Proof restriction functions....................................................................... 18
Chapter 4. Reflexive theories and proof restriction functions.............................. 24
Chapter 5. Truth definitions and formalized consistency proofs......................... 30
Chapter 6. Pair proof restriction functions............................................................... 37
Conclusions.................................................................................................................. 45
Bibliography................................................................................................................... 46
Słowa kluczowe
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 108
Liczba stron
47
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Opis fizyczny
Dissertationes Mathematicae, Tom CVIII
Daty
wydano
1973
Twórcy
autor
Bibliografia
  • [1] A. Church, An unsolvable problem of elementary number theory, Amer. J. Math. 68 (1936), pp. 346-363.
  • [2] W. Craig, On axiomatizability within a system, J. Symbolic Logic 18 (1953), pp. 30-32.
  • [3] M. Davis, An explicit Diophantine definition of the exponential function, (1971) not yet published.
  • [4] M. Davis, H. Putnam, and Julia Robinson, The decision problem for exponential Diophantine equations, Ann. of Math. 74 (1961), pp. 425-436.
  • [5] A. Ehrenfeucht and S. Feferman, Representability of recursively enumerable sets informal theories, Arch. Math. Logik Grundlagenforsch. 5 (1960), pp. 37-41.
  • [6] S. Feferman, Arithmetization of metamathematics in a general setting, Fund. Math. 49 (1960), pp. 36-92.
  • [7] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandler Systeme I, Monatsh. Math. Phys. 38 (1931), pp. 173-198.
  • [8] D. Jensen, Proof restriction functions for infinitely axiomatized theories, Dissertation, University of Southern California, Los Angeles (1971).
  • [9] S. C. Kleene, Finite axiomatizability of theories in the predicate calculus using additional predicate symbols. Two papers on the predicate calculus, Mem. Amer. Math Soc. 10 (1952), pp. 27-68.
  • [10] G. Kreisel and A. Lévy, Reflection principles and their use for establishing the complexity of axiomatic, systems, Zeitschr. Math. Logik 14 (1968), pp. 97-142.
  • [11] G. Kreisel and H. Wang, Some applications of formalized consistency proofs, Fund. Math. 42 (1966), pp. 101-1-10; II (Addition to the preceeding) Fund. Math. 46 (1968), pp, 334-336.
  • [12] A. Lévy, A. hierarchy of formulas in set theory, Mem. Amer. Math. Soc. 67 (1966).
  • [13] Yu. V. Matijasevič, Diophantine representation of recursively enumerable predicates, Proceedings of the Second Scandinavian Logic Symposium, Amsterdam 1971.
  • [14] R. Montague, Two contributions to tile foundations of set theory, Logic, Philosophy and Methodology of Science, Proc. 1960 Int. Congress, Stanford (1962), pp. 94-110.
  • [15] A. Mostowski, On models of axiomatic systems, Fund. Math. 39 (1962), pp. 133-168.
  • [16] J. B. Rosser, Extensions of some theorems of Gödell and Church, J. Symbolic Logic 1 (1936), pp. 87-91.
  • [17] Julia Robinson, Existential definability in arithmetic, Trans. Amer. Math. Soc. 72 (1962), pp. 437-449.
  • [18] J. Shoenfield, Mathematical Logic, Reading 1967.
  • [19] M. E. Szabo, od., The Collected Papers of Gerhard Gentzen, Amsterdam 1969.
  • [20] A. Tarski, Der Wahrheitsbegriffe in den formalisierten Sprachen, Studia Philos. 1 (1936), pp. 261-405.
  • [21] A. Tarski, A. Mostowski, and E. Robinson, Undecidable Theories, Amsterdam 1953 and 1968.
  • [22] H. Wang, The non-finitizability of impredicative principles, Proc. Nat. Acad. Sci. U. S. A. 36 (1950), pp. 479-484.
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