An algebraic approach to nonstandard analysis
In this paper we present the main features of Nonstandard Analysis without any use of Logic or any deep tool from set theory. The hyperreal numbers are introduced by three axioms of algebraic type whose consistency is proved by algebraic means. Probably this way of introducing Nonstandard Analysis, is not the most interesting and elegant. Moreover, part of the richness and the power of Nonstandard Analysis (as the Transfer and the Saturation Principles) are lost. Nevertheless, most of its elementary applications can be carried out without any problem. In order to show this, the last four sections of this paper are devoted to simple applications to Elementary Calculus.
KeywordsAlgebraic Approach Canonical Representation Ring Homomorphism Degree Theory Uniform Continuity
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