3 problems

Let $\varphi(x,y)$ be a partitioned formula. A formula is NTP$_2$ when it does not have the tree property of the second kind, and it is resilient in the sense used in the paper. ULC…

Definable extension conjecture. The formula $\phi(x;b)$ extends to an $M$-definable type.

Extensible definability conjecture. There is $\theta(y)\in \operatorname{tp}(d/M)$ such that the partial type