On ω 2 -saturated families

Lajos Soukup

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 355-359
  • ISSN: 0010-2628

Abstract

top
If there is no inner model with measurable cardinals, then for each cardinal λ there is an almost disjoint family 𝒜 λ of countable subsets of λ such that every subset of λ with order type ≥ ω 2 contains an element of 𝒜 λ .

How to cite

top

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
  1. 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. 
  2. 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
  3. 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
  4. Goldstern M., Judah H., Shelah S., Saturated families, and more on regular spaces omitting cardinals, preprint. MR1052573
  5. Hajnal A., Some results and problem on set theory, Acta Math. Acad. Sci. Hung. 11 (1960), 277-298. (1960) MR0150044
  6. Hajnal A., Juhász I., Soukup L., On saturated almost disjoint families, Comment. Math. Univ. Carolinae 28 (1987), 629-633. (1987) MR0928677
  7. Jech T., Set Theory, Academic Press, New York, 1978. Zbl1007.03002MR0506523
  8. 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.

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

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.