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.
Citation
B. Zilber. "Bi-coloured fields on the complex numbers." J. Symbolic Logic 69 (4) 1171 - 1186, December 2004. https://doi.org/10.2178/jsl/1102022217
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