| Title:
|
Perfect sets and collapsing continuum (English) |
| Author:
|
Repický, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
315-327 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Under Martin's axiom, collapsing of the continuum by Sacks forcing $\Bbb S$ is characterized by the additivity of Marczewski's ideal (see [4]). We show that the same characterization holds true if $\frak d=\frak c$ proving that under this hypothesis there are no small uncountable maximal antichains in $\Bbb S$. We also construct a partition of $^\omega 2$ into $\frak c$ perfect sets which is a maximal antichain in $\Bbb S$ and show that $s^0$-sets are exactly (subsets of) selectors of maximal antichains of perfect sets. (English) |
| Keyword:
|
Sacks forcing |
| Keyword:
|
Marczewski's ideal |
| Keyword:
|
cardinal invariants |
| MSC:
|
03E17 |
| MSC:
|
03E40 |
| MSC:
|
03E50 |
| MSC:
|
54A35 |
| idZBL:
|
Zbl 1104.03045 |
| idMR:
|
MR2026166 |
| . |
| Date available:
|
2009-01-08T19:29:28Z |
| Last updated:
|
2020-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119388 |
| . |
| 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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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
