Submission date: 27 November 2007

Abstract:

(in French) The Arithmetic is interpreted in all the groups of Richard Thompson and Graham Higman, as well as in other groups of piecewise affine permutations of an interval which generalize the groups of Thompson and Higman. In particular, the elementary theories of all these groups are undecidable. Moreover, the group F of Thompson and some of its generalizations interpret the Arithmetic without parameters.

Mathematics Subject Classification:

Keywords and phrases: Groupes de Thompson, groupe simple de présentation finie, théorie élémentaire, interprétation, arithmétique, décidabilité héréditaire.

Full text arXiv: pdf, ps.