Geodesic
Open and solved problems concerning polarized partition relations
Shimon Garti 1   ; Saharon Shelah 2
1 Institute of Mathematics The Hebrew University of Jerusalem Jerusalem 91904, Israel
2 Institute of Mathematics The Hebrew University of Jerusalem Jerusalem 91904, Israel and Department of Mathematics Rutgers University New Brunswick, NJ 08854, U.S.A.
Fundamenta Mathematicae, Tome 234 (2016) no. 1, pp. 1-14 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\alpha $ there exists a forcing notion $\mathbb {P}$ such that the strong polarized relation $\binom {\aleph _{\alpha +1}}{\aleph _\alpha } \rightarrow \binom {\aleph _{\alpha +1}}{\aleph _\alpha }^{1,1}_2$ holds in ${\rm \bf V}^{\mathbb {P}}$.
DOI : 10.4064/fm763-10-2015
Keywords: list problems concerning polarized partition relation solve couple showing every limit non inaccessible ordinal alpha there exists forcing notion mathbb strong polarized relation binom aleph alpha aleph alpha rightarrow binom aleph alpha aleph alpha holds mathbb

Shimon Garti  1   ; Saharon Shelah  2

1 Institute of Mathematics The Hebrew University of Jerusalem Jerusalem 91904, Israel
2 Institute of Mathematics The Hebrew University of Jerusalem Jerusalem 91904, Israel and Department of Mathematics Rutgers University New Brunswick, NJ 08854, U.S.A. 
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Shimon Garti; Saharon Shelah. Open and solved problems concerning polarized partition relations. Fundamenta Mathematicae, Tome 234 (2016) no. 1, pp. 1-14. doi: 10.4064/fm763-10-2015

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