Abstract
In his monograph, H. Gonshor showed that Conway’s real closed field of surreal numbers carries an exponential and logarithmic map. In this paper, we give a complete description of the exponential equivalence classes in the spirit of the additive and multiplicative equivalence classes. This description is made in terms of a recursive formula as well as a sign sequence formula for the family of representatives of minimal length of these exponential classes.
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We thank Joris van der Hoeven for providing valuable comments on a preliminary version of this article, and the referee for a very careful reading of the submitted manuscript.
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Kuhlmann, S., Matusinski, M. The Exponential-Logarithmic Equivalence Classes of Surreal Numbers. Order 32, 53–68 (2015). https://doi.org/10.1007/s11083-013-9315-3
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DOI: https://doi.org/10.1007/s11083-013-9315-3