Sh:903

• Machura, M., Shelah, S., & Tsaban, B. (2010). Squares of Menger-bounded groups. Trans. Amer. Math. Soc., 362(4), 1751–1764. arXiv: math/0611353 DOI: 10.1090/S0002-9947-09-05169-1 MR: 2574876
• Abstract:
  Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group \mathbb{Z}^{\mathbb{N}}, whose square is not Menger-bounded. This settles a major open problem concerning boundedness notions for groups and implies that Menger-bounded groups need not be Scheepers-bounded. This also answers some questions of Banakh, Nickolas, and Sanchis.
• Version 2007-02-08_11 (10p) published version (14p)

@article{Sh:903,
 author = {Machura, Micha{\l} and Shelah, Saharon and Tsaban, Boaz},
 title = {{Squares of Menger-bounded groups}},
 journal = {Trans. Amer. Math. Soc.},
 fjournal = {Transactions of the American Mathematical Society},
 volume = {362},
 number = {4},
 year = {2010},
 pages = {1751--1764},
 issn = {0002-9947},
 mrnumber = {2574876},
 mrclass = {54H11 (03E17 54C65)},
 doi = {10.1090/S0002-9947-09-05169-1},
 note = {\href{https://arxiv.org/abs/math/0611353}{arXiv: math/0611353}},
 arxiv_number = {math/0611353}
}