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On -saturated families
If there is no inner model with measurable cardinals, then for each cardinal there is an almost disjoint family of countable subsets of such that every subset of with order type contains an element of .
Soukup, Lajos. "On $\omega ^2$-saturated families." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 355-359. <http://eudml.org/doc/247267>.
@article{Soukup1991,
abstract = {If there is no inner model with measurable cardinals, then for each cardinal $\lambda $ there is an almost disjoint family $\mathcal \{A\}_\{\lambda \}$ of countable subsets of $\lambda $ such that every subset of $\lambda $ with order type $\ge \{\omega ^\{\scriptscriptstyle 2\}\}$ contains an element of $\mathcal \{A\}_\{\lambda \}$.},
author = {Soukup, Lajos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {almost disjoint; saturated family; refinement; large cardinals; saturated family; covering lemma for ; almost disjoint family; inner model with a measurable cardinal},
language = {eng},
number = {2},
pages = {355-359},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $\omega ^2$-saturated families},
url = {http://eudml.org/doc/247267},
volume = {32},
year = {1991},
}
TY - JOUR
AU - Soukup, Lajos
TI - On $\omega ^2$-saturated families
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 355
EP - 359
AB - If there is no inner model with measurable cardinals, then for each cardinal $\lambda $ there is an almost disjoint family $\mathcal {A}_{\lambda }$ of countable subsets of $\lambda $ such that every subset of $\lambda $ with order type $\ge {\omega ^{\scriptscriptstyle 2}}$ contains an element of $\mathcal {A}_{\lambda }$.
LA - eng
KW - almost disjoint; saturated family; refinement; large cardinals; saturated family; covering lemma for ; almost disjoint family; inner model with a measurable cardinal
UR - http://eudml.org/doc/247267
ER -
- Balcar B., Dočkálková J., Simon P., Almost disjoint families of countable sets, in Proc. Coll. Soc. J. Bolyai 37, Finite and Infinite Sets, Eger, 1981, vol I.
- Erdös P., Hajnal A., Unsolved problems in set theory, Proc. Symp. Pure Math., vol. 13, part 1, Am. Math. Soc., R. I. 1971, 17-48. MR0280381
- Erdös P., Hajnal A., Unsolved and solved problems in set theory, Proc Symp. Pure Math., vol. 25, Am. Math. Soc., R. I. 1971, 269-287. MR0357122
- Goldstern M., Judah H., Shelah S., Saturated families, and more on regular spaces omitting cardinals, preprint. MR1052573
- Hajnal A., Some results and problem on set theory, Acta Math. Acad. Sci. Hung. 11 (1960), 277-298. (1960) MR0150044
-
Hajnal A., Juhász I., Soukup L., On saturated almost disjoint families, Comment. Math. Univ. Carolinae 28 (1987), 629-633. (1987) MR0928677
- Jech T., Set Theory, Academic Press, New York, 1978. Zbl1007.03002MR0506523
- Komáth P., Dense systems of almost disjoint sets, in Proc. Coll. Soc. J. Bolyai 37, Finite and Infinite Sets, Eger, 1981, vol I.
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