Surreal substructures
Volume 266 / 2024
Fundamenta Mathematicae 266 (2024), 25-96
MSC: Primary 03C64; Secondary 03E20
DOI: 10.4064/fm231020-23-2
Published online: 1 July 2024
Abstract
Conway’s field $\mathbf{No}$ of surreal numbers comes both with a natural total order and an additional “simplicity relation” which is also a partial order. Considering $\mathbf{No}$ as a doubly ordered structure for these two orderings, an isomorphic copy of $\mathbf{No}$ inside itself is called a surreal substructure. It turns out that many natural subclasses of $\mathbf{No}$ 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.
