2 problems

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Basic trichotomy conjecture for definable sets in dp-rank 2 ordered Abelian groups
Let $\mathcal{R}$ be an expansion of a divisible ordered Abelian group of dp-rank $2$ . Consider infinite definable sets that are discrete, dense and codense in an interval, or Cant…
Conjectureopendefinable-sets dp-rank ordered-abelian-groupsarXiv posted 2 days ago
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Finite burden for finite dp-rank fields with finitely many valuation rings
Finite-dp-rank valuation conjecture. The structure $(K,\mathcal{O}_1,\ldots,\mathcal{O}_n)$ has finite burden.
Conjectureopendp-rank model-theory valued-fieldsarXiv posted 2 days ago

Basic trichotomy conjecture for definable sets in dp-rank 2 ordered Abelian groups