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.
This research was supported by the NSF Grant MCA 76-06484.
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References
S. Feferman and R. Vaught, "The first order properties of products of algebraic systems," Fund. Math. 47 (1959), 57–103.
Y. Gurevich, "Elementary properties of ordered abelian groups," AMS Translations, 46, 165–192.
W. Henson, C. Jockusch, C. Rubel, G. Takeuti, "First order topology," Dissertationes Math. 143(1977) 40pp.
A. Macintyre, "On the elementary theory of Banach algebras," Ann. Math. Logic 3 (1971), 239–269.
A. Macintyre, "Model-completeness for sheaves of structures," Fund. Math. 81 (1973), 73–89.
V. Weispfenning, "Elimination of quantifiers for subdirect products of structures," J. Alg. 36 (1975), 252–277.
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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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