Bulletin of Symbolic Logic 18 (3):368-381 (2012)

Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular for theories of valued fields.
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DOI 10.2178/bsl/1344861887
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A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.
On Definable Subsets of P-Adic Fields.Angus MacIntyre - 1976 - Journal of Symbolic Logic 41 (3):605-610.
Imaginaries in Real Closed Valued Fields.Timothy Mellor - 2006 - Annals of Pure and Applied Logic 139 (1):230-279.

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