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Interprétation de l'arithmétique dans certains groupes de permutations affines par morceaux d'un intervalle

Part of: Model theory Special aspects of infinite or finite groups Computability and recursion theory

Published online by Cambridge University Press:  30 January 2009

Tuna Altinel  and
Alexey Muranov
Tuna Altinel
Affiliation:
Université de Lyon, Université Lyon 1, Institut Camille Jordan CNRS UMR 5208, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France (altinel@math.univ-lyon1.fr)
Alexey Muranov
Affiliation:
Université de Lyon, Université Lyon 1, Institut Camille Jordan CNRS UMR 5208, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France (muranov@math.univ-toulouse.fr)
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Abstract

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, Thompson's group F and some of its generalizations interpret the arithmetic without parameters.

Résumé

L'arithmétique est interprétée dans tous les groupes de Richard Thompson et de Graham Higman, aussi bien que dans d'autres groupes des permutations affines par morceaux d'un intervalle qui généralisent les groupes de Thompson et de Higman. En particulier, les théories élémentaires de tous ces groupes sont indécidables. De plus, le groupe F de Thompson et certaines de ses généralisations interprètent l'arithmétique sans paramètres.

Keywords

groupes de Thompsongroupe simple de présentation finiethéorie élémentaireinterprétationarithmétiqueindécidabilité héréditaireThompson groupsfinitely presented simple groupselementary theoryinterpretationarithmetichereditary undecidability

MSC classification

Secondary: 03C62: Models of arithmetic and set theory 20F65: Geometric group theory 03D35: Undecidability and degrees of sets of sentences
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 4 , October 2009 , pp. 623 - 652
Copyright
Copyright © Cambridge University Press 2009

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