7 problems

Assume that $T$ is a first-order theory and that … with $2^\lambda=\lambda^+$. Let $\langle M_\alpha:\alpha<\lambda^+\rangle$ be a $\prec$-increasing continuous sequence with…

Generic pair conjecture. The theory $T$ is independent if and only if

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…

2-IP conjecture. Every IP field is necessarily $2$-IP.

Let ${\mathscr{F}}$ be an expansion of an infinite field $F$. A family ${\mathcal X}$ of subsets of $F$ is directed when any two members have a common member containing their union…

Let $\oplus$ and $\otimes$ be binary operations on $\mathbb{N}$ such that $(\mathbb{N},\oplus,\otimes)$ is a field. Ordered-field IP conjecture. The expansion…