Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-27T08:33:18.559Z Has data issue: false hasContentIssue false

Some elementary results in intuitionistic model theory

Published online by Cambridge University Press:  12 March 2014

Wim Veldman
Affiliation:
Mathematisch Instituut, Katholieke Universiteit, 6525 ED Nijmegen, The Netherlands, E-mail: veldman@sci.kun.nl
Frank Waaldijk
Affiliation:
Mathematisch Instituut, Katholieke Universiteit, 6525 ED Nijmegen, The Netherlands, E-mail: waaldijk@sci.kun.nl

Abstract

We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1996

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]Fraïssé, R., Cours de logique mathématique, Tome 2, Gauthier-Villars, Paris, 1972.Google Scholar
[2]Heyting, A., Intuiţionism, an introduction, North-Holland, Amsterdam, 1956, second revised edition, 1966; third revised edition, 1980.Google Scholar
[3]Hodges, W., Model theory, Cambridge University Press, 1993.CrossRefGoogle Scholar
[4]Kleene, S. C. and Vesley, R. E., The foundations of intuitionistic mathematics, especially in relation to recursive functions, North-Holland, Amsterdam, 1965.Google Scholar
[5]Mines, R., Richman, F., and Ruitenburg, W., A course in constructive algebra, Springer-Verlag, Berlin, 1988.CrossRefGoogle Scholar
[6]Troelstra, A. S. and van Dalen, D., Constructivism in mathematics, vol I and II, North-Holland, Amsterdam, 1988.Google Scholar
[7]van Dalen, D., The continuum and first-order intuitionistic logic, this Journal, vol. 57 (1993), pp. 14171424.Google Scholar
[8]Veldman, W. and Janssen, M., Some observations on intuitionistically elementary properties of linear orderings, Archive for Mathematical Logic, vol. 29 (1990), pp. 171187.CrossRefGoogle Scholar