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 automorphisminvariant subset of the field is countable or cocountable. 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 exponentialalgebraic closedness property using the density of the group governing the ambiguity with respect to the complex topology.
Original language  English 

Article number  72 
Journal  Selecta Mathematica 
Volume  25 
Issue number  5 
Early online date  13 Nov 2019 
DOIs  
Publication status  Published  Dec 2019 
Keywords
 AxSchanuel
 Complex exponentiation
 Quasiminimal
 Zilber conjecture
Profiles

Jonathan Kirby
 School of Mathematics  Reader
 Logic  Member
Person: Research Group Member, Academic, Teaching & Research