| Résume | Joint work with Kobi Peterzil.
Let G be a simple compact Lie group, for example G=SO_3(R). We consider the structure of definable sets in the subgroup G^00 of infinitesimal elements. In an aleph_0-saturated elementary extension of the real field, G^00 is the inverse image of the identity under the standard part map, so is definable in the corresponding valued field. We show that the pure group structure on G^00 recovers the valued field, making this a bi-interpretation. Hence the definable sets in the group are as rich as possible.
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