Surreal substructures

Vincent Bagayoko (1, 2) , Joris van der Hoeven (3, 2)

1 UMons - Université de Mons
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 CNRS - Centre National de la Recherche Scientifique

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.

Domaines: Logique en informatique [cs.LO]; Théorie des nombres [math.NT]

Vincent Bagayoko, Joris van der Hoeven. Surreal substructures. 2019. ⟨hal-02151377v1⟩