Submission date: 29 June 2006

Abstract:

We characterize those functions f:C -> C$ definable in o-minimal expansions of the reals for which the structure (C,+ ,f) is strongly minimal -- such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy -- an algebraically closed field is definable in certain strongly minimal structures which are definable in an o-minimal field.

Mathematics Subject Classification: 03C64; Secondary: 03C45, 12J15, 03C60,30Cxx

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