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

Abstract

We note that some form of the condition "$p_1,p_2$ have a ${\le }_{\mathbb{Q}}$-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.

revised version (after referee's comments)