Abstract
In consequent extension of Cantor’s theory of ordinal numbers 0, 1, 2, …ω,ω + 1, ω + 2, …ω・2, ω・2+1, ω・2+2, …… ω2, ……… , non-Archimedean number models for the real axis have been constructed by Sikorski [9] and, independently, Klaua [4, 5]. Reference [9] introduced integral and rational ordinal numbers; references [4, 5] introduced integral, rational, and real ordinal numbers. The purpose of these constructions is to extend the real axis into the transfinite, at the same time as refining it infinitesimally.
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