Conway's field of surreal numbers comes both with a natural total order and an additional “simplicity relation” which is also a partial order. Considering as a doubly ordered structure for these two orderings, an isomorphic copy of into itself is called a surreal substructure. It turns out that many natural subclasses of 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.

Authors: Vincent Bagayoko, Joris van der Hoeven

Keywords: surreal numbers, surreal substructures, group action, nested numbers

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