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Tomasz Weiss More remarks on the intersection ideal M ∩ N Comment.Math.Univ.Carolin. 59,3 (2018) 311 –316.

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Tomasz Weiss

More remarks on the intersection ideal M ∩ N

Comment.Math.Univ.Carolin. 59,3 (2018) 311 –316.

Abstract: We prove in ZFC that every M ∩ N additive set is N additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal M ∩ N , Comment.

Math. Univ. Carolin. 54 (2013), no. 3, 437–445] in the negative.

Keywords: intersection ideal M ∩ N ; null additive set; meager additive set AMS Subject Classification: 03E05, 03E17

References

[1] Bartoszy´nski T.,Remarks on small sets of reals, Proc. Amer. Math. Soc131(2003), no. 2, 625–630.

[2] Bartoszy´nski T., Judah H., Set Theory. On the Structure of the Real Line, A K Peters, Wellesley, 1995.

[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.

[4] Orenshtein T., Tsaban B.,Linear σ-additivity and some applications, Trans. Amer. Math.

Soc.363(2011), no. 7, 3621–3637.

[5] Pawlikowski J.,A characterization of strong measure zero sets, Israel J. Math.93(1996), 171–183.

[6] Weiss T.,A note on the intersection idealM∩N, Comment. Math. Univ. Carolin.54(2013), no. 3, 437–445.

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