On $\omega ^2$-saturated families

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 -

References

top

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. Zbl1007.03002 MR0506523
Komáth P., Dense systems of almost disjoint sets, in Proc. Coll. Soc. J. Bolyai 37, Finite and Infinite Sets, Eger, 1981, vol I.

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.