A note on the intersection ideal ℳ ∩ 𝒩

Tomasz Weiss

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 3, page 437-445
  • ISSN: 0010-2628

Abstract

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We prove among other theorems that it is consistent with Z F C that there exists a set X ⊆ 2 ω which is not meager additive, yet it satisfies the following property: for each F σ measure zero set F , X + F belongs to the intersection ideal ℳ ∩ 𝒩 .

How to cite

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Weiss, Tomasz. "A note on the intersection ideal $\mathcal {M}\cap \mathcal {N}$." Commentationes Mathematicae Universitatis Carolinae 54.3 (2013): 437-445. <http://eudml.org/doc/260682>.

@article{Weiss2013,
abstract = {We prove among other theorems that it is consistent with $ZFC$ that there exists a set $X\subseteq 2^\omega $ which is not meager additive, yet it satisfies the following property: for each $F_\sigma $ measure zero set $F$, $X+F$ belongs to the intersection ideal $\mathcal \{M\}\cap \mathcal \{N\}$.},
author = {Weiss, Tomasz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$F_\sigma $ measure zero sets; intersection ideal $\mathcal \{M\}\cap \mathcal \{N\}$; meager additive sets; sets perfectly meager in the transitive sense; $\gamma $-sets; measure-zero set; intersection ideal; meager additive set; -set},
language = {eng},
number = {3},
pages = {437-445},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on the intersection ideal $\mathcal \{M\}\cap \mathcal \{N\}$},
url = {http://eudml.org/doc/260682},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Weiss, Tomasz
TI - A note on the intersection ideal $\mathcal {M}\cap \mathcal {N}$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 3
SP - 437
EP - 445
AB - We prove among other theorems that it is consistent with $ZFC$ that there exists a set $X\subseteq 2^\omega $ which is not meager additive, yet it satisfies the following property: for each $F_\sigma $ measure zero set $F$, $X+F$ belongs to the intersection ideal $\mathcal {M}\cap \mathcal {N}$.
LA - eng
KW - $F_\sigma $ measure zero sets; intersection ideal $\mathcal {M}\cap \mathcal {N}$; meager additive sets; sets perfectly meager in the transitive sense; $\gamma $-sets; measure-zero set; intersection ideal; meager additive set; -set
UR - http://eudml.org/doc/260682
ER -

References

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