3 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…

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…