Open and solved problems concerning polarized partition relations

Shimon Garti; Saharon Shelah

Fundamenta Mathematicae, Tome 233 (2016), p. 1-14 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $(\binom{ℵ_{α + 1}}{ℵ_{α}}) \to {(\binom{ℵ_{α + 1}}{ℵ_{α}})}_{2}^{1, 1}$ holds in $V^{ℙ}$ .

Publié le : 2016-01-01

Zbl 06602778

EUDML-ID : urn:eudml:doc:286690

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     title = {Open and solved problems concerning polarized partition relations},
     journal = {Fundamenta Mathematicae},
     volume = {233},
     year = {2016},
     pages = {1-14},
     zbl = {06602778},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm763-10-2015}
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Shimon Garti; Saharon Shelah. Open and solved problems concerning polarized partition relations. Fundamenta Mathematicae, Tome 233 (2016) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm763-10-2015/