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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