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On some Axioms in Foundations of Cartesian Spaces

Published online by Cambridge University Press:  20 November 2018

Haragauri N. Gupta
Haragauri N. Gupta*
Affiliation:
University of Saskatchewan, Regina
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The present paper seeks to put into a clearer focus the roles of certain axioms in axiomatic studies of finite dimensional Cartesian spaces over various classes of ordered fields. Following Tarski [3], we define a Cartesian space as follows.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 831 - 836
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Gupta, H.N., An axiomatization of finite-dimensional Cartesian spaces over arbitrary ordered fields. Bull. Acad. Polon. Sci. 13 (1965) 550–551.Google Scholar
2. Scott, D., Dimension in elementary Euclidean geometry, in the axiomatic method. (Amsterdam, 1959) 53–67.Google Scholar
3. Tarski, A., What is elementary geometry? in the axiomatic method. (Amsterdam, 1959) 16–29.Google Scholar