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R.J. THOMPSON’S GROUPS F AND T ARE BI-INTERPRETABLE WITH THE RING OF THE INTEGERS
CLÉMENT LASSERRE
Journal:

The Journal of Symbolic Logic / Volume 79 / Issue 3 / September 2014

Published online by Cambridge University Press:

18 August 2014, pp. 693-711

Print publication:

September 2014
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We show that R.J. Thompson’s groups F and T are bi-interpretable with the ring of the integers. From a result by A. Khélif, these groups are quasi-finitely axiomatizable and prime. So, the group T provides an example of a simple group which is quasi-finitely axiomatizable and prime. This answers questions posed by T. Altınel and A. Muranov in [2], and by A. Nies in [12].

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R.J. THOMPSON’S GROUPS F AND T ARE BI-INTERPRETABLE WITH THE RING OF THE INTEGERS