Bi-coloured fields on the complex numbers

Journal of Symbolic Logic 69 (4):1171-1186 (2004)
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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.

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