Interpretation of the Arithmetic in certain groups of piecewise affine permutations of an interval
Group Theory
2009-09-14 v2 Logic
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.
Keywords
Cite
@article{arxiv.0807.1079,
title = {Interpretation of the Arithmetic in certain groups of piecewise affine permutations of an interval},
author = {Tuna Altınel and Alexey Muranov},
journal= {arXiv preprint arXiv:0807.1079},
year = {2009}
}
Comments
v2: 27 pages, 3 figures, minor corrections, English translation of arXiv:0711.3832v3; v1: 27 pages, 3 figures, English translation of arXiv:0711.3832v2