Model theory of analytic functions: some historical comments
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.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1344861887
Digital Object Identifier: doi:10.2178/bsl/1344861887
Zentralblatt MATH identifier: 06083932
Mathematical Reviews number (MathSciNet): MR2987521