top
We list some open problems concerning the polarized partition relation. We solve a couple of them, by showing that for every limit non-inaccessible ordinal α there exists a forcing notion ℙ such that the strong polarized relation holds in .
Shimon Garti, and Saharon Shelah. "Open and solved problems concerning polarized partition relations." Fundamenta Mathematicae 234.1 (2016): 1-14. <http://eudml.org/doc/286690>.
@article{ShimonGarti2016, abstract = {We list some open problems concerning the polarized partition relation. We solve a couple of them, by showing that for every limit non-inaccessible ordinal α there exists a forcing notion ℙ such that the strong polarized relation $\binom\{ℵ_\{α+1\}\}\{ℵ_\{α\}\} → \binom\{ℵ_\{α+1\}\}\{ℵ_\{α\}\}^\{1,1\}_\{2\}$ holds in $V^\{ℙ\}$.}, author = {Shimon Garti, Saharon Shelah}, journal = {Fundamenta Mathematicae}, keywords = {partition calculus; cardinal characteristics; pcf theory}, language = {eng}, number = {1}, pages = {1-14}, title = {Open and solved problems concerning polarized partition relations}, url = {http://eudml.org/doc/286690}, volume = {234}, year = {2016}, }
TY - JOUR AU - Shimon Garti AU - Saharon Shelah TI - Open and solved problems concerning polarized partition relations JO - Fundamenta Mathematicae PY - 2016 VL - 234 IS - 1 SP - 1 EP - 14 AB - We list some open problems concerning the polarized partition relation. We solve a couple of them, by showing that for every limit non-inaccessible ordinal α there exists a forcing notion ℙ such that the strong polarized relation $\binom{ℵ_{α+1}}{ℵ_{α}} → \binom{ℵ_{α+1}}{ℵ_{α}}^{1,1}_{2}$ holds in $V^{ℙ}$. LA - eng KW - partition calculus; cardinal characteristics; pcf theory UR - http://eudml.org/doc/286690 ER -