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

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

2007-11-26

arxiv.org/abs/0711.3832v3

Journal of the Institute of Mathematics of Jussieu, Volume 8, Issue 04, October 2009, pp. 623--652

Mathematics

Logic

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

Scientific paper

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.

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