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The hyperserial field of surreal numbers

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arxiv 2310.14873 v1 pith:W23ZDTP5 submitted 2023-10-23 math.LO

classification math.LO
keywords alphanumberssurrealfieldfunctionshyperserialomegaarchetypes
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abstract

For any ordinal $\alpha > 0$, we show how to define a hyperexponential $E_{\omega^{\alpha}}$ and a hyperlogarithm $L_{\omega^{\alpha}}$ on the class $\mathbf{No}^{>, \succ}$ of positive infinitely large surreal numbers. Such functions are archetypes of extremely fast and slowly growing functions at infinity. We also show that the surreal numbers form a so-called hyperserial field for our definition.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory

    math.LO 2025-01 conditional novelty 3.0 of 10

    Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.

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