Interpretation of the Arithmetic in certain groups of piecewise affine permutations of an interval

Details Interpretation of the Arithmetic in certain groups of piecewise affine permutations of an interval Interpretation of the Arithmetic in certain groups of piecewise affine permutations of an interval

2008-07-07

arxiv.org/abs/0807.1079v2

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

Mathematics

Group Theory

v2: 27 pages, 3 figures, minor corrections, English translation of arXiv:0711.3832v3; v1: 27 pages, 3 figures, English transla

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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