Creature forcing and large continuum: the joy of halving |
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Authors: | Jakob Kellner Saharon Shelah |
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Institution: | 1. Kurt G?del Research Center for Mathematical Logic, Universit?t Wien, W?hringer Stra?e 25, 1090, Vienna, Austria 2. Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel 3. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08854, USA
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Abstract: | For ${f,g\in\omega^\omega}$ let ${c^\forall_{f,g}}$ be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let ${c^\exists_{f,g}}$ be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that it is consistent that ${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\epsilon}$ for continuum many pairwise different cardinals ${\kappa_\epsilon}$ and suitable pairs ${(f_\epsilon,g_\epsilon)}$ . For the proof we introduce a new mixed-limit creature forcing construction. |
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