2 problems

Let $P$ be a class forcing notion. A forcing notion is almost $\lambda_0,\lambda$-periodic if it is $\lambda_0,\lambda$-periodic in a set-generic extension of the universe, where…

Let $T$ be a dependent complete first-order theory, let $M$ be a saturated model of cardinality $\kappa>|T|$, and let $\bold I=\langle a_\alpha:\alpha<\kappa\rangle$ be an indiscer…