# Sacks forcing collapses $\U0001d520$ to $\U0001d51f$

Commentationes Mathematicae Universitatis Carolinae (1993)

- Volume: 34, Issue: 4, page 707-710
- ISSN: 0010-2628

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topSimon, Petr. "Sacks forcing collapses $\mathfrak {c}$ to $\mathfrak {b}$." Commentationes Mathematicae Universitatis Carolinae 34.4 (1993): 707-710. <http://eudml.org/doc/247505>.

@article{Simon1993,

abstract = {We shall prove that Sacks algebra is nowhere $(\mathfrak \{b\}, \mathfrak \{c\}, \mathfrak \{c\})$-distributive, which implies that Sacks forcing collapses $\mathfrak \{c\}$ to $\mathfrak \{b\}$.},

author = {Simon, Petr},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {perfect tree; distributivity of Boolean algebra; almost disjoint refinement; tree; cardinal; Sacks algebra; Sacks forcing},

language = {eng},

number = {4},

pages = {707-710},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Sacks forcing collapses $\mathfrak \{c\}$ to $\mathfrak \{b\}$},

url = {http://eudml.org/doc/247505},

volume = {34},

year = {1993},

}

TY - JOUR

AU - Simon, Petr

TI - Sacks forcing collapses $\mathfrak {c}$ to $\mathfrak {b}$

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1993

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 34

IS - 4

SP - 707

EP - 710

AB - We shall prove that Sacks algebra is nowhere $(\mathfrak {b}, \mathfrak {c}, \mathfrak {c})$-distributive, which implies that Sacks forcing collapses $\mathfrak {c}$ to $\mathfrak {b}$.

LA - eng

KW - perfect tree; distributivity of Boolean algebra; almost disjoint refinement; tree; cardinal; Sacks algebra; Sacks forcing

UR - http://eudml.org/doc/247505

ER -

## References

top- Abraham U., A minimal model for $\neg $CH: iteration of Jensen’s reals, Trans. Amer. Math. Soc. (1984), 281 657-674. (1984) MR0722767
- Balcar B., Simon P., Disjoint Refinement, in: Handbook of Boolean Algebra, Elsevier Sci. Publ. (1989), 333-386. (1989) MR0991597
- Judah H., Miller A.W., Shelah S., Sacks forcing, Laver forcing and Martin's axiom, Arch. Math. Logic (1992), 31 145-161. (1992) Zbl0755.03026MR1147737
- Rosłanowski A., Shelah S., More forcing notions imply diamond, (preprint January 4, 1993).
- Sacks G.E., Forcing with perfect closed sets, Axiomatic set theory, Proc. Symp. Pure Math. 13 (1971), 331-355. (1971) Zbl0226.02047MR0276079

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