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- W2949260784 abstract "We present a unifying theory of with certain classes of analytic functions, called with analytic structure. Both real closed and Henselian valued are considered. For real closed with analytic structure, o-minimality is shown. For Henselian valued fields, both the model theory and the analytic theory are developed. We give a list of examples that comprises, to our knowledge, all principal, previously studied, analytic structures on Henselian valued fields, as well as new ones. The b-minimality is shown, as well as other properties useful for motivic integration on valued fields. The paper is reminiscent of [Denef, van den Dries, and real subanalytic sets Ann. of Math. (2) 128 (1988) 79--138], of [Cohen, Paul J. Decision procedures for real and p-adic fields Comm. Pure Appl. Math. 22 (1969) 131--151, and of [Fresnel, van der Put, Rigid analytic geometry and its applications Progress in Mathematics, 218 Birkhauser (2004)], and unifies work by van den Dries, Haskell, Macintyre, Macpherson, Marker, Robinson, and the authors." @default.
- W2949260784 created "2019-06-27" @default.
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- W2949260784 date "2009-08-17" @default.
- W2949260784 modified "2023-09-23" @default.
- W2949260784 title "Fields with Analytic Structure" @default.
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