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On Order in a Plane

Published online by Cambridge University Press:  20 November 2018

H. G. Forder
H. G. Forder*
Affiliation:
The University of Auckland, Auckland, New Zealand
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When a set of axioms is laid down as the basis of any mathematical doctrine, it must be proved that this set never leads to a contradiction. In this note we turn the question around. A set of axioms is given and we wish to adjoin an axiom of a specified type. How far does the demand of non-contradiction limit the choice of the new axiom?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 997 - 1000
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Forder, H. G., The foundations of Euclidean geometry (1927) (Dover reprint, 1958).Google Scholar
2. Geiger, M., Systematische Axiomatik (1924).Google Scholar