Another proof of a result of Jech and Shelah
Czechoslovak Mathematical Journal (2013)
- Volume: 63, Issue: 3, page 577-582
- ISSN: 0011-4642
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topKomjáth, Péter. "Another proof of a result of Jech and Shelah." Czechoslovak Mathematical Journal 63.3 (2013): 577-582. <http://eudml.org/doc/260605>.
@article{Komjáth2013,
abstract = {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.},
author = {Komjáth, Péter},
journal = {Czechoslovak Mathematical Journal},
keywords = {partially ordered set; pcf theory; partially ordered set; pcf theory},
language = {eng},
number = {3},
pages = {577-582},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Another proof of a result of Jech and Shelah},
url = {http://eudml.org/doc/260605},
volume = {63},
year = {2013},
}
TY - JOUR
AU - Komjáth, Péter
TI - Another proof of a result of Jech and Shelah
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 577
EP - 582
AB - 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.
LA - eng
KW - partially ordered set; pcf theory; partially ordered set; pcf theory
UR - http://eudml.org/doc/260605
ER -
References
top- Jech, T., Shelah, S., 10.2307/2275613, J. Symb. Log. 61 (1996), 313-317. (1996) Zbl0878.03036MR1380692DOI10.2307/2275613
- Shelah, S., Laflamme, C., Hart, B., 10.1016/0168-0072(93)90033-A, Ann. Pure Appl. Logic 64 (1993), 169-194. (1993) Zbl0788.03046MR1241253DOI10.1016/0168-0072(93)90033-A
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