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

Published online by Cambridge University Press:  18 August 2014

CLÉMENT LASSERRE
CLÉMENT LASSERRE*
Affiliation:
ÉQUIPE DE LOGIQUE MATHÉMATIQUE UNIVERSITÉ PARIS DIDEROT PARIS 7 UFR DE MATHÉMATIQUES CASE 7012 SITE CHEVALERET 75205 PARIS CEDEX 13, FRANCE
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Abstract

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].

Keywords

Primary 03C6003C62Secondary 20F65Thompson’s groupssimple groupsQFA groupsprime groupsbi-interpretability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 3 , September 2014 , pp. 693 - 711
Copyright
Copyright © The Association for Symbolic Logic 2014 

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