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Preprint Number 931
931. Yimu Yin
On polynomial-bounded T-convex fields
Submission date: 25 September 2015.
We propose to grok the first-order theories TCVF of polynomial-bounded T-convex fields in a two-sorted language and prove some basic results concerning definable sets, mainly in the field sort. In particular, we show: under some mild assumptions on the o-minimal theory T, TCVF admits quantifier elimination; certain class of partial differential operators almost commute with the reduction map (to the residue field); all definable functions are piecewise infinitesimally Lipschitz continuous; etc.
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