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 and some of its generalizations interpret the Arithmetic without parameters.
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