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Rings of continuous functions: Decision problems

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

Abstract

R=C(X,R) is the ring of continuous functions from the topological space X to the real field

Theorem I. If X is a nondiscrete metric space then second order arithmetic is interpretable in R.

Theorem II. If X is the Stone-Cech compactification of a discrete set then the theory of R is decidable.

Keywords

  • Global Function
  • Basic Formula
  • Function Term
  • Function Quantifier
  • Reducible Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported by the NSF Grant MCA 76-06484.

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© 1980 Springer-Verlag

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Cherlin, G. (1980). Rings of continuous functions: Decision problems. 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/BFb0090160

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  • DOI: https://doi.org/10.1007/BFb0090160

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10269-4

  • Online ISBN: 978-3-540-38393-2

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