'A Test of Efficiency'. Schröder´s Application of His Algebra of relatives to Set-Theory

LEGRIS, JAVIER

Heidelberg (Alemania)

Jornada; Jahrestagung 2004 der Deutschen Mathematiker Vereinigung (DMV 2004); 2004

Deutsche Mathematiker Vereinigung

“A Test of Efficiency”. Schröder´s Application of His Algebra of Relatives to Set-Theory AMS-Klassifikation: 03-03, 01A55 Javier Legris University of Buenos Aires and CONICET (Argentina) e-mail: jlegris@mail.retina.ar ----------------------------- Abstract The aim of this paper is to analyze the motivations of Ernst Schröder in applying his algebra of relatives to Dedekind´s theory of chains and to Cantor´s theory of set equivalence. In lecture IX of volume III of his Vorlesungen über die Algebra der Logik and in his paper ``Note über die Algebra der binären Relative´´, Schröder applied the algebra of relatives to Dedekind´s theory of chains. This application of the algebra of relatives would serve as ``test of its efficiency´´. Later, in his paper ´´On Two Definitions of finity and Cantor´s theorems´´, he devoted to Cantor´s set theory, trying to prove by means of the algebra of relatives the result about set equivalence that was called sometimes Cantor-Schröder-Bernstein theorem. Schröder stressed the following advantages of his symbolization: (1) more generality, (2) the possibility of ´shortcuts´ in the proofs, (3) Greater expressiveness of the notation. So, it will be shown that pragmatics reasons motivated Schröder to carry out these applications. They are related with the intended universality of the algebra of relatives.