| Title:
|
A tree $\pi $-base for $\Bbb R^\ast$ without cofinal branches (English) |
| Author:
|
Hernández-Hernández, Fernando |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
721-734 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove an analogue to Dordal's result in P.L. Dordal, {\it A model in which the base-matrix tree cannot have cofinal branches\/}, J. Symbolic Logic {\bf 52} (1980), 651--664. He obtained a model of ZFC in which there is a tree $\pi$-base for $\Bbb N^{\ast}$ with no $\omega_{2}$ branches yet of height $\omega_{2}$. We establish that this is also possible for $\Bbb R^{\ast}$ using a natural modification of Mathias forcing. (English) |
| Keyword:
|
distributivity of Boolean algebras |
| Keyword:
|
cardinal invariants of the continuum |
| Keyword:
|
Stone-Čech compactification |
| Keyword:
|
tree $\pi$-base |
| MSC:
|
03E17 |
| MSC:
|
06E15 |
| MSC:
|
54A35 |
| MSC:
|
54G05 |
| idZBL:
|
Zbl 1121.54057 |
| idMR:
|
MR2259502 |
| . |
| Date available:
|
2009-05-05T16:54:37Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119562 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| . |
