15 citations · 17 across the 5 of their papers we have counts for
6 papers
Integration on the Surreals
Ovidiu Costin, Philip Ehrlich
Conway's real closed field of surreal numbers is a sweeping generalization of the real numbers and the ordinals to which a number of elementary functions such as log…
Surreal ordered exponential fields
Philip Ehrlich, Elliot Kaplan
In [26], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway's ordered field of surreal numbers was brought to the fore and employed to pr…
Contemporary Infinitesimalist Theories of Continua and their late 19th- and early 20th-century forerunners
Philip Ehrlich
The purpose of this paper is to provide a historical overview of some of the contemporary infinitesimalist alternatives to the Cantor-Dedekind theory of continua. Among the theorie…
Homogeneous Universal H-fields
Lou van den Dries, Philip Ehrlich
We consider derivations on Conway's field of surreal numbers such that the ordered differential field has constant field $\mathbb{…
Number Systems with Simplicity Hierarchies II
Philip Ehrlich, Elliot Kaplan
In [15], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway's ordered field No of surreal numbers was brought to the fore and employed to provide neces…
Integration on the Surreals: a Conjecture of Conway, Kruskal and Norton
Ovidiu Costin, Philip Ehrlich, Harvey M. Friedman
In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field No of surreal numbers containing the reals and the ordinals, as well as a vast array of less fami…