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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On extensions of models of strong fragments of arithmetic
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by Roman Kossak PDF
Proc. Amer. Math. Soc. 108 (1990), 223-232 Request permission

Correction: Proc. Amer. Math. Soc. 112 (1991), 913-914.


Using a weak notion of recursive saturation (not always semiregularity) we prove that there are no finitely generated countable models of $B\Sigma _n { + \neg I{\Sigma _n}( {n > 0} )}$. We consider the problem of not almost semiregularity of models of $I{\Sigma _n} + \neg B{\Sigma _{n + 1}}$ . From a partial solution to this problem we deduce a generalization of the theorem of Smorynski and Stavi on cofinal extensions of recursively saturated models of arithmetic.
  • P. Clote, Partition relations in arithmetic, Methods in mathematical logic (Caracas, 1983) Lecture Notes in Math., vol. 1130, Springer, Berlin, 1985, pp. 32–68. MR 799036, DOI 10.1007/BFb0075306
  • Peter G. Clote, A note on the MacDowell-Specker theorem, Fund. Math. 127 (1987), no. 2, 163–170. MR 882624, DOI 10.4064/fm-127-2-163-170
  • Haim Gaifman and Constantine Dimitracopoulos, Fragments of Peano’s arithmetic and the MRDP theorem, Logic and algorithmic (Zurich, 1980) Monograph. Enseign. Math., vol. 30, Univ. Genève, Geneva, 1982, pp. 187–206. MR 648303
  • L. A. S. Kirby and J. B. Paris, Initial segments of models of Peano’s axioms, Set theory and hierarchy theory, V (Proc. Third Conf., Bierutowice, 1976) Lecture Notes in Math., Vol. 619, Springer, Berlin, 1977, pp. 211–226. MR 0491157
  • Roman Kossak, A certain class of models of Peano arithmetic, J. Symbolic Logic 48 (1983), no. 2, 311–320. MR 704085, DOI 10.2307/2273548
  • —, Models with the $\omega$-property, to appear in Journal of Symbolic Logic.
  • David W. Kueker, Back-and-forth arguments and infinitary logics, Infinitary logic: in memoriam Carol Karp, Lecture Notes in Math., Vol. 492, Springer, Berlin, 1975, pp. 17–71. MR 0462940
  • H. Lessan, Models of arithmetic, Ph.D. Thesis, Manchester 1978.
  • J. B. Paris, Some conservation results for fragments of arithmetic, Model theory and arithmetic (Paris, 1979–1980) Lecture Notes in Math., vol. 890, Springer, Berlin-New York, 1981, pp. 251–262. MR 645006
  • J. B. Paris and L. A. S. Kirby, $\Sigma _{n}$-collection schemas in arithmetic, Logic Colloquium ’77 (Proc. Conf., Wrocław, 1977) Studies in Logic and the Foundations of Mathematics, vol. 96, North-Holland, Amsterdam-New York, 1978, pp. 199–209. MR 519815
  • J. Paris and A. Wilkie, A note on the end extension problem, (to appear).
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 223-232
  • MSC: Primary 03F30; Secondary 03C62, 03H15
  • DOI:
  • MathSciNet review: 984802