Sacks forcing collapses 𝔠 to 𝔟

Petr Simon

Commentationes Mathematicae Universitatis Carolinae (1993)

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

Abstract

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We shall prove that Sacks algebra is nowhere ( 𝔟 , 𝔠 , 𝔠 ) -distributive, which implies that Sacks forcing collapses 𝔠 to 𝔟 .

How to cite

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Simon, 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

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  1. Abraham U., A minimal model for ¬ CH: iteration of Jensen’s reals, Trans. Amer. Math. Soc. (1984), 281 657-674. (1984) MR0722767
  2. Balcar B., Simon P., Disjoint Refinement, in: Handbook of Boolean Algebra, Elsevier Sci. Publ. (1989), 333-386. (1989) MR0991597
  3. 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
  4. Rosłanowski A., Shelah S., More forcing notions imply diamond, (preprint January 4, 1993). 
  5. 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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