English

Interpr\'etation de l'Arithm\'etique dans certains groupes de permutations affines par morceaux d'un intervalle

Logic 2022-03-28 v3 Group Theory

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 FF and some of its generalizations interpret the Arithmetic without parameters.

Keywords

Cite

@article{arxiv.0711.3832,
  title  = {Interpr\'etation de l'Arithm\'etique dans certains groupes de permutations affines par morceaux d'un intervalle},
  author = {Tuna Altınel and Alexey Muranov},
  journal= {arXiv preprint arXiv:0711.3832},
  year   = {2022}
}

Comments

v3: French, 29 pages, 3 figures, minor corrections; v2: 29 pages, 3 figures, corrections, added references, no essential changes; v1: 28 pages, 3 figures

R2 v1 2026-06-21T09:46:52.845Z