The tree property at the double successor of a singular cardinal with a larger gap |
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Authors: | Sy-David Friedman Radek Honzik Šárka Stejskalová |
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Affiliation: | 1. Kurt Gödel Research Center for Mathematical Logic, Währinger Strasse 25, 1090 Vienna, Austria;2. Charles University, Department of Logic, Celetná 20, Praha 1, 116 42, Czech Republic |
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Abstract: | Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, , and the tree property holds at . Next we generalize this result to an arbitrary cardinal μ such that and . This result provides more information about possible relationships between the tree property and the continuum function. |
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Keywords: | 03E35 03E55 The tree property Singular cardinals |
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