Forcing axioms for $λ$ -complete $μ^+$ -C.C

preprint2020arXivOpen access

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 $λ$ -complete $μ^+$ -c.c. forcing notions. We also show some versions are really stronger than others.

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Forcing axioms for $λ$ -complete $μ^+$ -C.C

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Forcing axioms for λλλ-complete μ+μ^+μ+-C.C

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Forcing axioms for $λ$ -complete $μ^+$ -C.C