Submission date: 13 May 2019

Abstract:

We prove that an expansion of an algebraically closed field by n arbitrary valuation rings is NTP_2, and in fact has finite burden. It fails to be NIP, however, unless the valuation rings form a chain. Moreover, the incomplete theory of algebraically closed fields with n valuation rings is decidable.

Mathematics Subject Classification: 03C10, 03C45

Keywords and phrases:

Full text arXiv 1905.04991: pdf, ps.