Blurred Complex Exponentiation

Kirby, Jonathan (2019) Blurred Complex Exponentiation. Selecta Mathematica, 25. ISSN 1022-1824

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: math.lo,03c65 (primary),03c48 (secondary)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: LivePure Connector
Date Deposited: 23 Jan 2020 02:49
Last Modified: 18 Mar 2020 01:02
URI: https://ueaeprints.uea.ac.uk/id/eprint/73748
DOI: 10.1007/s00029-019-0517-4

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