Submission date: 6 December 2018

Abstract:

We show quantifier elimination theorems for real closed valued fields with separated analytic structure and overconvergent analytic structure in their natural one-sorted languages and deduce that such structures are weakly o-minimal. We also provide a short proof that algebraically closed valued fields with separated analytic structure (in any rank) are C-minimal.

Mathematics Subject Classification: Primary 32P05, 32B05, 32B05, 03C10, 03C64, Secondary 14P10

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Full text arXiv 1812.02490: pdf, ps.