More remarks on the intersection ideal 𝒩

Tomasz Weiss

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 3, page 311-316
  • ISSN: 0010-2628

Abstract

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We prove in ZFC that every 𝒩 additive set is 𝒩 additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal 𝒩 , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437-445] in the negative.

How to cite

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Weiss, Tomasz. "More remarks on the intersection ideal ${\mathcal {M}}\cap {\mathcal {N}}$." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 311-316. <http://eudml.org/doc/294400>.

@article{Weiss2018,
abstract = {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.},
author = {Weiss, Tomasz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {intersection ideal $\{\mathcal \{M\}\}\cap \{\mathcal \{N\}\}$; null additive set; meager additive set},
language = {eng},
number = {3},
pages = {311-316},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {More remarks on the intersection ideal $\{\mathcal \{M\}\}\cap \{\mathcal \{N\}\}$},
url = {http://eudml.org/doc/294400},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Weiss, Tomasz
TI - More remarks on the intersection ideal ${\mathcal {M}}\cap {\mathcal {N}}$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 3
SP - 311
EP - 316
AB - 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.
LA - eng
KW - intersection ideal ${\mathcal {M}}\cap {\mathcal {N}}$; null additive set; meager additive set
UR - http://eudml.org/doc/294400
ER -

References

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  1. Bartoszyński T., 10.1090/S0002-9939-02-06567-X, Proc. Amer. Math. Soc 131 (2003), no. 2, 625–630. MR1933355DOI10.1090/S0002-9939-02-06567-X
  2. Bartoszyński T., Judah H., Set Theory. On the Structure of the Real Line, A K Peters, Wellesley, 1995. MR1350295
  3. Goldstern M., Kellner J., Shelah S., Wohofsky W., 10.1090/S0002-9947-2013-05783-2, Trans. Amer. Math. Soc. 366 (2014), no. 1, 245–307. MR3118397DOI10.1090/S0002-9947-2013-05783-2
  4. Orenshtein T., Tsaban B., 10.1090/S0002-9947-2011-05228-1, Trans. Amer. Math. Soc. 363 (2011), no. 7, 3621–3637. MR2775821DOI10.1090/S0002-9947-2011-05228-1
  5. Pawlikowski J., 10.1007/BF02761100, Israel J. Math. 93 (1996), 171–183. Zbl0857.28001MR1380640DOI10.1007/BF02761100
  6. Weiss T., A note on the intersection ideal 𝒩 , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437–445. MR3090421

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