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Preprint Number 1799

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1799. Raymond McCulloch
A nondefinability result for expansions of the ordered real field by the Weierstrass ℘ function

Submission date: 12 June 2020


Suppose that Ω is a complex lattice that is closed under complex conjugation and that I is a small real interval, and that D is a disc in ℂ. Then the restriction ℘|_D is definable in the structure (ℝ̄,℘|_I) if and only if the lattice Ω has complex multiplication. This characterises lattices with complex multiplication in terms of definability.

Mathematics Subject Classification:

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Full text arXiv 2006.07437: pdf, ps.

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