Forcing axioms for $\lambda$-complete $\mu^+$-C.C

29 Jul 2020 · Shelah Saharon ·

We note that some form of the condition "$p_1, p_2$ have a $\leq_{\mathbb{Q}}$-lub in $\mathbb{Q}$" is necessary in some forcing axiom for $\lambda$-complete $\mu^+$-c.c. forcing notions. We also show some versions are really stronger than others.