Richard Dedekind y la arquitectura del continuo aritm\'etico

TL;DR

This paper argues that Richard Dedekind exhibited structuralist tendencies early in his career, significantly contributing to the conceptual framework of the arithmetical continuum before the 20th-century formalist movement.

Contribution

It reveals Dedekind's early structuralist style in his 1854 dissertation, highlighting his role in shaping the architecture of the arithmetical continuum.

Findings

Dedekind's 1854 dissertation shows early structuralist tendencies.

Dedekind significantly influenced the development of the arithmetical continuum.

The paper challenges the view that structuralism only emerged in the 20th century.

Abstract

It is usually considered that the structuralist tendency in mathematics began in the twentieth century, at some point after the works on set theory and obtained its spreading through the works made by the Bourbaki group. In the present paper we argument the presence of this stylistic inclination in Richard Dedekind (1831-1916) when he made this dissertation for the habilitation as privatdozent at the University of Goettingen in 1854. Our main objective is to show how evolved the structuralist style in Dedekind's works, and to argument why we consider him significant to the architecture of arithmetical continuum.