Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-17T17:13:55.506Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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