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

by Shelah. [Sh:1036]

We note that some form of the condition ``p_1, p_2 have a leq_{{Q}}-lub in {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, a strong way to answer Alexie's question of having {P} satisfying one condition but no {P}' equivalent to {P} satisfying another. We have not looked systematically whether any such question (of interest) is open. [Ask Ashutosh to read in Aug 2014]; B. check counterexmple in [SHSt:154, page 235], and one in Ap section 2 or 3 of [SH:f]; check the paper with Otmar- have another variant

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