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Bi-coloured fields on the complex numbers

Published online by Cambridge University Press:  12 March 2014

B. Zilber
B. Zilber*
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St, Giles Oxford OX1 3LB., UK, E-mail: zilber@maths.ox.ac.uk
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Abstract.

We consider two theories of “bad fields” constructed by B.Poizat using Hrushovski's amalgamation and show that these theories have natural models representable as the field of complex numbers with a distinguished subset given as a union of countably many real analytic curves. One of the two examples is based on the complex exponentiation and the proof assumes Schanuel's conjecture.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 4 , December 2004 , pp. 1171 - 1186
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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