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We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)].
Andrzej Rosłanowski, and Saharon Shelah. "Around cofin." Colloquium Mathematicae 134.2 (2014): 211-225. <http://eudml.org/doc/283860>.
@article{AndrzejRosłanowski2014, abstract = {We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)].}, author = {Andrzej Rosłanowski, Saharon Shelah}, journal = {Colloquium Mathematicae}, keywords = {cardinal invariants; Borel ideals; cofin; forcing}, language = {eng}, number = {2}, pages = {211-225}, title = {Around cofin}, url = {http://eudml.org/doc/283860}, volume = {134}, year = {2014}, }
TY - JOUR AU - Andrzej Rosłanowski AU - Saharon Shelah TI - Around cofin JO - Colloquium Mathematicae PY - 2014 VL - 134 IS - 2 SP - 211 EP - 225 AB - We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)]. LA - eng KW - cardinal invariants; Borel ideals; cofin; forcing UR - http://eudml.org/doc/283860 ER -