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Preprint Number 1221

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1221. Jonathan Kirby
Blurred Complex Exponentiation

Submission date: 12 May 2017


It is shown that the complex field equipped with the “approximate exponential map”, defined up to ambiguity from a small group, is quasiminimal: every automorphism-invariant subset of the field is countable or co-countable. If the ambiguity is taken to be from a subfield analogous to a field of constants then the resulting “blurred exponential field” is isomorphic to the result of an equivalent blurring of Zilber's exponential field, and to a suitable reduct of a differentially closed field. These results are progress towards Zilber's conjecture that the complex exponential field itself is quasiminimal. A key ingredient in the proofs is to prove the analogue of the exponential-algebraic closedness property using the density of the group governing the ambiguity with respect to the complex topology.

Mathematics Subject Classification: 03C65 (Primary), 03C48 (Secondary)

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Full text arXiv 1705.04574: pdf, ps.

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