13 found
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  1.  5
    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.
    We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.
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  2.  6
    Decisive Creatures and Large Continuum.Jakob Kellner & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (1):73-104.
    For f, g $ \in \omega ^\omega $ let $c_{f,g}^\forall $ be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch v of the f-tree, one of the g-trees contains v. $c_{f,g}^\exists $ is the dual notion: For every branch v, one of the g-trees guesses v(m) infinitely often. It is consistent that $c_{f \in ,g \in }^\exists = c_{f \in ,g \in }^\forall = k_ \in $ for N₁ many (...)
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  3.  3
    New Reals: Can Live with Them, Can Live Without Them.Martin Goldstern & Jakob Kellner - 2006 - Mathematical Logic Quarterly 52 (2):115-124.
    We give a self-contained proof of the preservation theorem for proper countable support iterations known as “tools-preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals.
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  4.  15
    Preserving Preservation.Jakob Kellner & Saharon Shelah - 2005 - Journal of Symbolic Logic 70 (3):914 - 945.
    We prove that the property "P doesn't make the old reals Lebesgue null" is preserved under countable support iterations of proper forcings, under the additional assumption that the forcings are nep (a generalization of Suslin proper) in an absolute way. We also give some results for general Suslin ccc ideals.
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  5.  18
    Even More Simple Cardinal Invariants.Jakob Kellner - 2008 - Archive for Mathematical Logic 47 (5):503-515.
    Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.
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  6.  11
    Creature Forcing and Large Continuum: The Joy of Halving.Jakob Kellner & Saharon Shelah - 2012 - Archive for Mathematical Logic 51 (1-2):49-70.
    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 (...)
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  7.  23
    More on the Pressing Down Game.Jakob Kellner & Saharon Shelah - 2011 - Archive for Mathematical Logic 50 (3-4):477-501.
    We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: consistently, there is a nowhere precipitous normal ideal I on ${\aleph_2}$ such that player nonempty wins the pressing down game of length ${\aleph_1}$ on I even if player empty starts.
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  8.  20
    Preserving Non-Null with Suslin+ Forcings.Jakob Kellner - 2006 - Archive for Mathematical Logic 45 (6):649-664.
    We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive nep forcing (e.g. P is Suslin+) and P does not make any I-positive Borel set small, then P does not make any I-positive set small.
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  9.  7
    Winning the Pressing Down Game but Not Banach-Mazur.Jakob Kellner, Matti Pauna & Saharon Shelah - 2007 - Journal of Symbolic Logic 72 (4):1323 - 1335.
    Let S be the set of those α ∈ ω₂ that have cofinality ω₁. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length ω₁, but not the Banach-Mazur game of length ω + 1 (both games starting with S).
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  10.  2
    Compact Cardinals and Eight Values in Cichoń’s Diagram.Jakob Kellner, Anda Ramona Tănasie & Fabio Elio Tonti - 2018 - Journal of Symbolic Logic 83 (2):790-803.
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  11.  27
    Saccharinity.Jakob Kellner & Saharon Shelah - 2011 - Journal of Symbolic Logic 76 (4):1153-1183.
    We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. As an application, we introduce a new method to force (weak) measurability of all definable sets with respect to a certain (non-ccc) ideal.
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  12.  8
    Pitowsky’s Kolmogorovian Models and Super-Determinism.Jakob Kellner - 2017 - Foundations of Physics 47 (1):132-148.
    In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed “spin- functions” and later “Kolmogorovian models”, which employs a nonstandard notion of probability. We describe Pitowsky’s analysis and argue that his notion of hidden variables is in fact just super-determinism. Pitowsky’s first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue (...)
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  13.  10
    A Sacks Real Out of Nowhere.Jakob Kellner & Saharon Shelah - 2010 - Journal of Symbolic Logic 75 (1):51-76.
    There is a proper countable support iteration of length ω adding no new reals at finite stages and adding a Sacks real in the limit.
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