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Surreal substructures

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arxiv 2305.02001 v1 pith:2HIKHI7X submitted 2023-05-03 math.LO

Vincent Bagayoko , Joris van der Hoeven This is my paper · ORCID
classification math.LO
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Conway's field No of surreal numbers comes both with a natural total order and an additional "simplicity relation" which is also a partial order. Considering No as a doubly ordered structure for these two orderings, an isomorphic copy of No into itself is called a surreal substructure. It turns out that many natural subclasses of No are actually of this type. In this paper, we study various constructions that give rise to surreal substructures and analyze important examples in greater detail.

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  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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