Sur un article de 1954 sign\'e N. Cuesta, une traduction

TL;DR

This paper provides a French translation of N. Cuesta's 1954 work on ordered sets, exploring their construction, completion, and early mention of surreal numbers predating Conway's formal definition.

Contribution

It introduces a translation of Cuesta's pioneering work on ordered sets, highlighting early insights into surreal numbers and methods for constructing and completing ordered structures.

Findings

Early mention of surreal numbers before Conway

Methods for constructing ordered sets from families

Completion of ordered sets using Dedekind-like tools

Abstract

A translation from Spanish into French of a paper by N. Cuesta published in 1954. The paper deals mainly with partially, and totally, ordered sets. Two subjects are specially dealt with: Construction of new ordered sets starting from a family of those. Completion of ordered sets by tools akin to Dedekind cuts. Curiously enough, the so-called surreal numbers (later defined by Conway, in 1974) are already there, thirty years before.