Finite burden in multivalued algebraically closed fields
classification
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keywords
algebraicallyclosedringsvaluationburdenfieldsfinitearbitrary
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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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