Some model theory of compact Lie groups

We consider questions of first order definability in a compact Lie group G . Our main result is that if such G is simple (and centerless) then the Lie group structure of G is first order definable from the abstract group structure. Along the way we also show (i) if G is non-Abelian and connected then a copy of the field 11t is interpretable. in (G, ), and (ii) any "1-dimensional" field interpretable in (11t, +, ) is definably (i.e., semialgebraically) isomorphic to the ground field 11t.