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perfect tree; distributivity of Boolean algebra; almost disjoint refinement
We shall prove that Sacks algebra is nowhere $(\frak b, \frak c, \frak c)$-distributive, which implies that Sacks forcing collapses $\frak c$ to $\frak b$.
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[BS] Balcar B., Simon P.: Disjoint Refinement. in: Handbook of Boolean Algebra, Elsevier Sci. Publ. (1989), 333-386. MR 0991597
[JMS] Judah H., Miller A.W., Shelah S.: Sacks forcing, Laver forcing and Martin's axiom. Arch. Math. Logic (1992), 31 145-161. MR 1147737 | Zbl 0755.03026
[RS] Rosłanowski A., Shelah S.: More forcing notions imply diamond. (preprint January 4, 1993).
[S] Sacks G.E.: Forcing with perfect closed sets. Axiomatic set theory, Proc. Symp. Pure Math. 13 (1971), 331-355. MR 0276079 | Zbl 0226.02047
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