| Title:
|
More remarks on the intersection ideal ${\mathcal{M}}\cap {\mathcal{N}}$ (English) |
| Author:
|
Weiss, Tomasz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
311-316 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove in ZFC that every ${\mathcal{M}}\cap {\mathcal{N}}$ additive set is ${\mathcal{N}}$ additive, thus we solve Problem 20 from paper [Weiss T., {A note on the intersection ideal ${\mathcal{M}}\cap {\mathcal{N}}$}, Comment. Math. Univ. Carolin. {54} (2013), no. 3, 437-445] in the negative. (English) |
| Keyword:
|
intersection ideal ${\mathcal{M}}\cap {\mathcal{N}}$ |
| Keyword:
|
null additive set |
| Keyword:
|
meager additive set |
| MSC:
|
03E05 |
| MSC:
|
03E17 |
| idZBL:
|
Zbl 06940872 |
| idMR:
|
MR3861554 |
| DOI:
|
10.14712/1213-7243.2015.252 |
| . |
| Date available:
|
2018-09-10T12:08:56Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147399 |
| . |
| Reference:
|
[1] Bartoszyński T.: Remarks on small sets of reals.Proc. Amer. Math. Soc 131 (2003), no. 2, 625–630. MR 1933355, 10.1090/S0002-9939-02-06567-X |
| Reference:
|
[2] Bartoszyński T., Judah H.: Set Theory. On the Structure of the Real Line.A K Peters, Wellesley, 1995. MR 1350295 |
| Reference:
|
[3] Goldstern M., Kellner J., Shelah S., Wohofsky W.: Borel conjecture and dual Borel conjecture.Trans. Amer. Math. Soc. 366 (2014), no. 1, 245–307. MR 3118397, 10.1090/S0002-9947-2013-05783-2 |
| Reference:
|
[4] Orenshtein T., Tsaban B.: Linear $\sigma$-additivity and some applications.Trans. Amer. Math. Soc. 363 (2011), no. 7, 3621–3637. MR 2775821, 10.1090/S0002-9947-2011-05228-1 |
| Reference:
|
[5] Pawlikowski J.: A characterization of strong measure zero sets.Israel J. Math. 93 (1996), 171–183. Zbl 0857.28001, MR 1380640, 10.1007/BF02761100 |
| Reference:
|
[6] Weiss T.: A note on the intersection ideal ${\mathcal{M}}\cap {\mathcal{N}}$.Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437–445. MR 3090421 |
| . |
