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Sacks forcing collapses $${\mathfrak c}$$ to $${\mathfrak b}$$. (English) Zbl 0797.03053
The author improves some result of A. Roslanowski and S. Shelah and answers a question from their paper. The main result is that a Sacks algebra is nowhere $$({\mathfrak b},{\mathfrak c},{\mathfrak c})$$-distributive, which implies that Sacks forcing collapses $$\mathfrak c$$ to $$\mathfrak b$$.

##### MSC:
 03E40 Other aspects of forcing and Boolean-valued models 03C25 Model-theoretic forcing 03E25 Axiom of choice and related propositions 06A07 Combinatorics of partially ordered sets 06E05 Structure theory of Boolean algebras
##### Keywords:
tree; cardinal; Sacks algebra; Sacks forcing
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