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
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Keywords | Creature forcing Large Continuum Cardinal Characteristics Slaloms |
Categories | (categorize this paper) |
ISBN(s) | |
DOI | 10.1007/s00153-011-0253-8 |
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References found in this work BETA
Many Simple Cardinal Invariants.Martin Goldstern & Saharon Shelah - 1993 - Archive for Mathematical Logic 32 (3):203-221.
Decisive Creatures and Large Continuum.Jakob Kellner & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (1):73-104.
Even More Simple Cardinal Invariants.Jakob Kellner - 2008 - Archive for Mathematical Logic 47 (5):503-515.
Citations of this work BETA
Creature Forcing and Five Cardinal Characteristics in Cichoń’s Diagram.Arthur Fischer, Martin Goldstern, Jakob Kellner & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):1045-1103.
Many Different Covering Numbers of Yorioka’s Ideals.Noboru Osuga & Shizuo Kamo - 2014 - Archive for Mathematical Logic 53 (1-2):43-56.
On Cardinal Characteristics of Yorioka Ideals.Miguel A. Cardona & Diego A. Mejía - 2019 - Mathematical Logic Quarterly 65 (2):170-199.
Specialising Aronszajn Trees by Countable Approximations.Heike Mildenberger & Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (7):627-647.
Specializing Aronszajn Trees with Strong Axiom A and Halving.Heike Mildenberger & Saharon Shelah - 2019 - Notre Dame Journal of Formal Logic 60 (4):587-616.
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