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Simultaneous reflection and impossible ideals. (English) Zbl 1270.03068
Summary: We prove that if \(\mu^+\rightarrow[\mu^+]^2_{\mu^+}\) holds for a singular cardinal \(\mu\), then any collection of fewer than cf\((\mu)\) stationary subsets of \(\mu^+\) must reflect simultaneously.

MSC:
03E02 Partition relations
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References:
[1] Handbook of set theory 2 pp 1229– (2010)
[2] Getting more colors (2009)
[3] DOI: 10.4064/fm202-2-1 · Zbl 1168.03034
[4] Walks on ordinals and their characteristics 263 (2007)
[5] DOI: 10.1007/BF02392561 · Zbl 0658.03028
[6] Cardinal arithmetic 29 (1994) · Zbl 0848.03025
[7] DOI: 10.1016/j.apal.2010.02.004 · Zbl 1223.03027
[8] Handbook of set theory 1 pp 93– (2010)
[9] The higher infinite (1994)
[10] Set theory 48 (1999)
[11] Handbook of set theory 3 (2010)
[12] Combinatorial set theory: partition relations for cardinals 106 (1984) · Zbl 0573.03019
[13] Successors of singular cardinals and coloring theorems. II 74 pp 1287– (2009) · Zbl 1181.03047
[14] DOI: 10.1007/BF02783304 · Zbl 0657.03028
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