Fri, 29 Feb 2008
14:15
14:15
L3
Arithmetic in groups of piece-wise affine permutations of an interval
Alexey Muranov
(Lyon)
Abstract
Bardakov and Tolstykh have recently shown that Richard Thompson's group
$F$ interprets the Arithmetic $(\mathbb Z,+,\times)$ with parameters. We
consider a class of infinite groups of piecewise affine permutations of
an interval which contains all the three groups of Thompson and some
classical families of finitely presented infinite simple groups. We have
interpreted the Arithmetic in all the groups of this class. In particular
we have obtained that the elementary theories of all these groups are
undecidable. Additionally, we have interpreted the Arithmetic in $F$ and
some of its generalizations without parameters.
This is a joint work with Tuna Altınel.