| Title:
|
Property $(a)$ and dominating families (English) |
| Author:
|
da Silva, Samuel Gomes |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
667-684 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Generalizations of earlier negative results on Property $(a)$ are proved and two questions on an $(a)$-version of Jones' Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions ``$2^\omega$ is regular'' and ``$2^\omega < 2^{\omega_1}$'' the existence of a $T_1$ separable locally compact $(a)$-space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants such as $\frak d$ to prove results in the class of locally compact spaces that strengthen, in such class, the negative results mentioned above. (English) |
| Keyword:
|
property $(a)$ |
| Keyword:
|
dominating families |
| Keyword:
|
small cardinals |
| Keyword:
|
inner models of measurability |
| MSC:
|
03E04 |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1121.54014 |
| idMR:
|
MR2259498 |
| . |
| Date available:
|
2009-05-05T16:54:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119558 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
