In the beginning of the 1990's, Dehornoy, investigating selfdistributive systems, constructed a linear ordering on Artin's braid groups. Selfdistributive systems are sets equipped with a binary law satisfying the identity x(yz) = (xy)(xz). Such systems came up in the study of a large cardinal axiom in set theory. In this talk (which is an Eglish version of the talk I gave on 20 November 1999 at a Bourbaki Seminar in Paris) I present Dehornoy's work and its unexpected link with set theory. I also survey a recent geometric construction of Dehornoy's ordering by Fenn, Greene, Rolfsen, Rourke and Wiest.
The text of the talk is available in French on the Web as a gzipped postscript file or dvi file.