Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-02T03:26:59.431Z Has data issue: false hasContentIssue false
  • English
  • Français

Axioms for constructive fields

Published online by Cambridge University Press:  17 April 2009

John Staples
John Staples
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In constructive mathematics the Dedekind cut definition of real number is not equivalent to the definition of real number by Cauchy sequences, and the Dedekind real numbers do not satisfy Heyting's axioms for constructive fields. A more general notion of constructive field is proposed which includes the Dedekind real numbers; some linear algebra is given which applies to such fields.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 2 , April 1973 , pp. 221 - 232
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bishop, Errett, Foundations of constructive analysis (McGraw-Hill, New York; Toronto, Ontario; London; 1967).Google Scholar
[2]Heyting, A., “Untersuchungen über intuitionistische Algebra”, Verh. Nederl. Akad. Wetensch., Afd. Natuurk. Sect. 1 18, no. 2 (1941), 1–36.Google Scholar
[3]Mirsky, L., An introduction to linear algebra (Clarendon Press, Oxford, 1955).Google Scholar
[4]Staples, John, “On constructive fields”, Proc. London Math. Soc. (3) 23 (1971), 753–768.CrossRefGoogle Scholar