4 problems

Burden formula.

Let $T$ be an $\text{NTP}_2$ theory, and let burden be the model-theoretic rank on partial types. A rank is sub-additive if the burden of a concatenated tuple is at most the sum of…

Let $K$ be an ultraproduct of $p$-adic fields, in the pure ring language or the $RV$ language. Burden-one conjecture. Every such ultraproduct has burden $1$: … In the Denef–Pas lan…

In a first-order theory $T$, let $\operatorname{bdn}(a)$ denote the burden of a tuple $a$, and say that $T$ is NTP$_2$ when it has no inp-pattern of depth $\omega$ in a single vari…