# The Absolute Arithmetic Continuum and the Unification Of all Numbers Great and Small

@article{Ehrlich2012TheAA, title={The Absolute Arithmetic Continuum and the Unification Of all Numbers Great and Small}, author={Philip Ehrlich}, journal={The Bulletin of Symbolic Logic}, year={2012}, volume={18}, pages={1 - 45} }

Abstract In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including −ω, ω/2, 1/ω, and ω − π to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG (von Neumann–Bernays–Gödel set theory…

## 59 Citations

### An algebraic (set) theory of surreal numbers, I

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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 familiar numbers. A…

### Integration on the Surreals

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The class of surreal numbers, denoted byNo, initially proposed by Conway, is a universal ordered eld in the sense that any ordered eld can be embedded in it. They include in particular the real…

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An extension of the ring of scalar quantities, from the usual field of real numbers to a non-Archimedean, sometimes permits to simplify some problems which, at a first sight, may seem not correlated…

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This sequel to [16], analogous results for ordered abelian groups and ordered domains are established and it is shown that the theories of nontrivial divisible ordering groups, ordered fields, and real-closed ordered fields are the sole theories that are isomorphic to initial subgroups and initial subfields of ${\bf{No}}.

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