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arXiv · 1905.04991

Finite burden in multivalued algebraically closed fields

Will Johnson
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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.

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Will Johnson. 2019-05-13. Finite burden in multivalued algebraically closed fields. https://arxiv.org/abs/1905.04991

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