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Decidability of Scott's model as an ordered ℚ-vectorspace

Published online by Cambridge University Press:  12 March 2014

Miklós Erdélyi-Szabó
Miklós Erdélyi-Szabó*
Affiliation:
Department of Mathematics, Cornell University, White Hall, Ithaca, NY 14853, USA, E-mail: mszabo@math.cornell.edu
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Abstract

Let L = 〈<, +, hq, 1〉q∈ℚ where ℚ is the set of rational numbers and hq is a one-place function symbol corresponding to multiplication by q. Then the L-theory of Scott's model for intuitionistic analysis is decidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 3 , September 1997 , pp. 917 - 924
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1]Bishop, E., Foundations of constructive analysis, McGraw-Hill, 1967.Google Scholar
[2]Erdélyi-Szabó, M., Decidability in the constructive theory of reals as an ordered ℚ-vectorspace, Ph.D. thesis.Google Scholar
[3]Rabin, M. O., Decidability of second order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 1–35.Google Scholar
[4]Scott, D. S., Extending the topological interpretation to intuitionistic analysis, Compositio Mathematica, vol. 20 (1968), pp. 194–210.Google Scholar
[5]Scott, D. S., Extending the topological interpretation to intuitionistic analysis, II, Intuitionism and proof theory (Kino, A., Myhill, J., and Vesley, R. E., editors), North-Holland, Amsterdam, 1970, pp. 235–255.Google Scholar
[6]Scowcroft, P., The real algebraic structure of Scott's model of intuitionistic analysis, Annals of Pure and Applied Logic, vol. 27 (1984), pp. 275–308.CrossRefGoogle Scholar
[7]Scowcroft, P., More on real algebra in Scott's model, Annals of Pure and Applied Logic, vol. 30 (1986), pp. 277–291.CrossRefGoogle Scholar
[8]Scowcroft, P., A transfer theorem in constructive real algebra, Annals of Pure and Applied Logic, vol. 40 (1988), pp. 29–87.CrossRefGoogle Scholar
[9]Scowcroft, P., A new model for intuitionistic analysis, Annals of Pure and Applied Logic, vol. 47 (1990), pp. 145–165.CrossRefGoogle Scholar