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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.

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  • [1] Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR 0424560
  • [2] Jon Barwise and John Schlipf, On recursively saturated models of arithmetic, Model theory and algebra (A memorial tribute to Abraham Robinson), Springer, Berlin, 1975, pp. 42–55. Lecture Notes in Math., Vol. 498. MR 0409172
  • [3] H. Jerome Keisler, Models with tree structures, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348. MR 0357108
  • [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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