| Title:
|
Another proof of a result of Jech and Shelah (English) |
| Author:
|
Komjáth, Péter |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
577-582 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Shelah's pcf theory describes a certain structure which must exist if $\aleph _{\omega }$ is strong limit and $2^{\aleph _\omega }>\aleph _{\omega _1}$ holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordered set, and then we show by a straightforward, elementary (i.e., non-metamathematical) argument that such partially ordered sets exist. (English) |
| Keyword:
|
partially ordered set |
| Keyword:
|
pcf theory |
| MSC:
|
03E05 |
| idZBL:
|
Zbl 06282098 |
| idMR:
|
MR3125642 |
| DOI:
|
10.1007/s10587-013-0040-2 |
| . |
| Date available:
|
2013-10-07T11:55:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143476 |
| . |
| Reference:
|
[1] Jech, T., Shelah, S.: Possible pcf algebras.J. Symb. Log. 61 (1996), 313-317. Zbl 0878.03036, MR 1380692, 10.2307/2275613 |
| Reference:
|
[2] Shelah, S., Laflamme, C., Hart, B.: Models with second order properties V: A general principle.Ann. Pure Appl. Logic 64 (1993), 169-194. Zbl 0788.03046, MR 1241253, 10.1016/0168-0072(93)90033-A |
| . |
