Creature forcing and large continuum: the joy of halving

Archive for Mathematical Logic 51 (1-2):49-70 (2012)

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
Keywords Creature forcing  Large Continuum  Cardinal Characteristics  Slaloms
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DOI 10.1007/s00153-011-0253-8
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References found in this work BETA

Decisive Creatures and Large Continuum.Jakob Kellner & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (1):73-104.
Many Simple Cardinal Invariants.Martin Goldstern & Saharon Shelah - 1993 - Archive for Mathematical Logic 32 (3):203-221.
Even More Simple Cardinal Invariants.Jakob Kellner - 2008 - Archive for Mathematical Logic 47 (5):503-515.

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Citations of this work BETA

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On Cardinal Characteristics of Yorioka Ideals.Miguel A. Cardona & Diego A. Mejía - 2019 - Mathematical Logic Quarterly 65 (2):170-199.

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