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A hierarchy of cuts in models of arithmetic

Part of the Lecture Notes in Mathematics book series (LNM,volume 834)

Abstract

In this paper we show that it is possible to classify most of the natural families of cuts considered to date in terms of a single hierarchy. This classification gives conservation and independence results for fragments of arithmetic.

Keywords

  • Initial Segment
  • Winning Strategy
  • Peano Arithmetic
  • Satisfaction Relation
  • Reflection Principle

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References

  1. C. Dimitracopoulos, Doctorial thesis, Manchester. To appear.

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  2. J. Ketonen & R. Solovay, "Rapidly growing Ramsey functions", to appear.

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  3. L. Kirby, "Initial segments of models of arithmetic", Doctorial thesis, Manchester, 1977.

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  4. L. Kirby & J. Paris, "Initial segments of models of Peano’s axioms". Springer-Verlag lecture notes in mathematics, Vol. 619.

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  5. G. Mills, "Extensions of models of Peano arithmetic" Doctorial thesis, Berkeley, 1977.

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  6. J. Paris, "Some independence results for Peano arithmetic", J.S.L. 43 (1978), pp. 725–731.

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  7. J. Paris & L. Harrington, "An incompleteness in Peano arithmetic". Handbook for Mathematical Logic, (ed. J. Barwise.), North Holland, 1976, pp.1133–1142.

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  8. J. Paris & L. Kirby, "Σn-collection schemas in arithmetic". Logic Colloquium ’77, North Holland 1978, pp.199–209.

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© 1980 Springer-Verlag

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Paris, J.B. (1980). A hierarchy of cuts in models of arithmetic. In: Pacholski, L., Wierzejewski, J., Wilkie, A.J. (eds) Model Theory of Algebra and Arithmetic. Lecture Notes in Mathematics, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090171

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  • DOI: https://doi.org/10.1007/BFb0090171

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10269-4

  • Online ISBN: 978-3-540-38393-2

  • eBook Packages: Springer Book Archive