# Sh:972

- Rosłanowski, A., & Shelah, S. (2014).
*Monotone hulls for \mathcal N\cap\mathcal M*. Period. Math. Hungar.,**69**(1), 79–95. arXiv: 1007.5368 DOI: 10.1007/s10998-014-0042-3 MR: 3269711 -
Abstract:

Using the method of decisive creatures ([KrSh:872]) we show the consistency of “there is no increasing \omega_2–chain of Borel sets and {\rm non}({\mathcal N})= {\rm non}({\mathcal M})=\omega_2=2^\omega”. Hence, consistently, there are no monotone hulls for the ideal {\mathcal M}\cap {\mathcal N}. This answers Balcerzak and Filipczak. Next we use FS iteration with partial memory to show that there may be monotone Borel hulls for the ideals {\mathcal M}, {\mathcal N} even if they are not generated by towers. - published version (17p)

Bib entry

@article{Sh:972, author = {Ros{\l}anowski, Andrzej and Shelah, Saharon}, title = {{Monotone hulls for $\mathcal N\cap\mathcal M$}}, journal = {Period. Math. Hungar.}, fjournal = {Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society}, volume = {69}, number = {1}, year = {2014}, pages = {79--95}, issn = {0031-5303}, doi = {10.1007/s10998-014-0042-3}, mrclass = {03E17 (03E15 03E35)}, mrnumber = {3269711}, mrreviewer = {Diego Alejandro Mej\'ia}, doi = {10.1007/s10998-014-0042-3}, note = {\href{https://arxiv.org/abs/1007.5368}{arXiv: 1007.5368}}, arxiv_number = {1007.5368} }