9 problems

Let $T$ be a simple theory, and let two elements fork. A relation has the independence property if it witnesses the independence property. Stable-witness conjecture. If two element…

Let $T$ be a theory without the strict order property. Say that a relation witnesses the independence property if it has the independence property, and say that a relation witnesse…

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…

A theory $T$ is called NTP$_2$ if it has no formula with the tree property of the second kind. The Uniform Local Character over Finite Sets conjecture. Every NTP$_2$ theory satisfi…

Existence conjecture for NSOP$_1$ theories. Every NSOP$_1$ theory has existence.

Stable forking conjecture. If $p(x)$ forks over $A$, then some stable formula belonging to $p$ forks over $A$.

Let $T$ be a complete theory in a language $L$, and let $\mathfrak{C}$ be its monster model. A formula $\varphi(x,y)$, for disjoint tuples of variables $x$ and $y$, is stable if th…

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