Submission date: 19 September 2008

Abstract:

In this paper we prove, without assuming Schanuel's conjecture, that the E-subring generated by a real number not definable without parameters in the real exponential field is freely generated. We also obtain a similar result for the complex exponential field.

Mathematics Subject Classification: 03C64; 11D61

Keywords and phrases: O-minimal structures, E-rings

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