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Proceedings of the American Mathematical Society

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



A rather classless model

Author: Matt Kaufmann
Journal: Proc. Amer. Math. Soc. 62 (1977), 330-333
MSC: Primary 02H20
MathSciNet review: 0476498
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Abstract: Using $ {\diamondsuit _{{\omega _1}}}$, a model $ \mathfrak{N}$ of Peano arithmetic is constructed which has a unique extension $ (\mathfrak{N},\chi )$ to a model of $ \Delta _1^1$-PA, Peano arithmetic with $ \Delta _1^1$-comprehension.

References [Enhancements On Off] (What's this?)

  • [1] K. J. Barwise, Admissible sets and structures, Springer-Verlag, Heidelberg, 1975. MR 0424560 (54:12519)
  • [2] K. J. Barwise and J. Schlipf, On recursively saturated models of arithmetic, Model Theory and Algebra, Lecture Notes in Math., vol. 498, Springer-Verlag, Berlin, 1976, 42-55. MR 0409172 (53:12934)
  • [3] H. J. Keisler, Models with tree structures, Proc. Tarski Sympos., Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, R.I., 1974, pp. 331-348. MR 0357108 (50:9576)
  • [4] J. Schlipf, Some hyperelementary aspects of model theory, Doctoral Dissertation, University of Wisconsin, Madison, Wis., 1975.

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Keywords: Recursively saturated model, Peano arithmetic, $ \Delta _1^1$-comprehension, $ {\diamondsuit _{{\omega _1}}}$, Barwise Compactness Theorem, Barwise Completeness Theorem, $ HY{P_\mathfrak{N}}$, $ KP{U^ + }$
Article copyright: © Copyright 1977 American Mathematical Society

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