| Title:
|
On $\omega^2$-saturated families (English) |
| Author:
|
Soukup, Lajos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
355-359 |
| . |
| Category:
|
math |
| . |
| Summary:
|
If there is no inner model with measurable cardinals, then for each cardinal $\lambda $ there is an almost disjoint family $\Cal A_{\lambda}$ of countable subsets of $\lambda $ such that every subset of $\lambda $ with order type $\geq {\omega^{\scriptscriptstyle2}}$ contains an element of $\Cal A_{\lambda}$. (English) |
| Keyword:
|
almost disjoint |
| Keyword:
|
saturated family |
| Keyword:
|
refinement |
| Keyword:
|
large cardinals |
| MSC:
|
03E05 |
| MSC:
|
03E35 |
| MSC:
|
03E55 |
| idZBL:
|
Zbl 0755.03027 |
| idMR:
|
MR1137796 |
| . |
| Date available:
|
2009-01-08T17:44:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116976 |
| . |
| Reference:
|
[{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. |
| Reference:
|
[{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. MR 0280381 |
| Reference:
|
[{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. MR 0357122 |
| Reference:
|
[{4}] Goldstern M., Judah H., Shelah S.: Saturated families, and more on regular spaces omitting cardinals.preprint. MR 1052573 |
| Reference:
|
[{5}] Hajnal A.: Some results and problem on set theory.Acta Math. Acad. Sci. Hung. 11 (1960), 277-298. MR 0150044 |
| Reference:
|
[{6}] Hajnal A., Juhász I., Soukup L.: On saturated almost disjoint families.Comment. Math. Univ. Carolinae 28 (1987), 629-633. MR 0928677 |
| Reference:
|
[{7}] Jech T.: Set Theory.Academic Press, New York, 1978. Zbl 1007.03002, MR 0506523 |
| Reference:
|
[{8}] Komáth P.: Dense systems of almost disjoint sets.in Proc. Coll. Soc. J. Bolyai 37, Finite and Infinite Sets, Eger, 1981, vol I. |
| . |
