Surreal numbers, derivations and transseries
Copyright policy )Surreal numbers, derivations and transseries
Several authors have conjectured that Conway’s field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, that is, the derivation is surjective.
differential fields, 03C64, 16W60, 04A10, 26A12, 13N15, Surreal numbers, FOS: Mathematics, Surreal numbers, Hardy fields, Mathematics - Logic, Logic (math.LO), transseries, Hardy fields
differential fields, 03C64, 16W60, 04A10, 26A12, 13N15, Surreal numbers, FOS: Mathematics, Surreal numbers, Hardy fields, Mathematics - Logic, Logic (math.LO), transseries, Hardy fields
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