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Preprint Number 2299
2299. Olivier Bournez and Quentin Guilmant Surreal fields stable under exponential, logarithmic, derivative and anti-derivative functions E-mail: Submission date: 25 October 2022 Abstract: The class of surreal numbers, denoted by No, initially proposed by
Conway, is a universal ordered field in the sense that any ordered field can be
embedded in it. They include in particular the real numbers and the ordinal
numbers. They have strong relations with other fields such as field of
transseries. Following Gonshor, surreal numbers can be seen as signs sequences
of ordinal length, with some exponential and logarithmic functions that extend
the usual functions over the reals. No can actually be seen as an
elegant (generalized) power series field with real coefficients, namely Hahn
series with exponents in No itself. Mathematics Subject Classification: 12H05, 12J15 Keywords and phrases: |
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