| Title:
|
Sacks forcing collapses $\frak c$ to $\frak b$ (English) |
| Author:
|
Simon, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
707-710 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall prove that Sacks algebra is nowhere $(\frak b, \frak c, \frak c)$-distributive, which implies that Sacks forcing collapses $\frak c$ to $\frak b$. (English) |
| Keyword:
|
perfect tree |
| Keyword:
|
distributivity of Boolean algebra |
| Keyword:
|
almost disjoint refinement |
| MSC:
|
03C25 |
| MSC:
|
03E25 |
| MSC:
|
03E40 |
| MSC:
|
03G05 |
| MSC:
|
06A07 |
| MSC:
|
06E05 |
| idZBL:
|
Zbl 0797.03053 |
| idMR:
|
MR1263799 |
| . |
| Date available:
|
2009-01-08T18:07:32Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118627 |
| . |
| Reference:
|
[A] Abraham U.: A minimal model for $\lnot$CH: iteration of Jensen's reals.Trans. Amer. Math. Soc. (1984), 281 657-674. MR 0722767 |
| Reference:
|
[BS] Balcar B., Simon P.: Disjoint Refinement.in: Handbook of Boolean Algebra, Elsevier Sci. Publ. (1989), 333-386. MR 0991597 |
| Reference:
|
[JMS] Judah H., Miller A.W., Shelah S.: Sacks forcing, Laver forcing and Martin's axiom.Arch. Math. Logic (1992), 31 145-161. Zbl 0755.03026, MR 1147737 |
| Reference:
|
[RS] Rosłanowski A., Shelah S.: More forcing notions imply diamond.(preprint January 4, 1993). |
| Reference:
|
[S] Sacks G.E.: Forcing with perfect closed sets.Axiomatic set theory, Proc. Symp. Pure Math. 13 (1971), 331-355. Zbl 0226.02047, MR 0276079 |
| . |
