2011
DOI: 10.1007/s00153-011-0253-8
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Creature forcing and large continuum: the joy of halving

Abstract: Abstract. For f, g ∈ ω ω let c ∀ 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 ∃ 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 ∃ fǫ ,gǫ = c ∀ fǫ ,gǫ = κ ǫ for continuum many pairwise different cardinals κ ǫ and suitable pairs ( f ǫ , g ǫ ). For the proof we introduce a new mixed-limit creature… Show more

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Cited by 13 publications
(13 citation statements)
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“…• the width norm; 12 As usual, if the logarithm results in a negative number, or if we apply the logarithm to a negative number, we instead define the resulting norm to be 0. So really we mean nor…”
Section: Definition 253mentioning
confidence: 99%
“…• the width norm; 12 As usual, if the logarithm results in a negative number, or if we apply the logarithm to a negative number, we instead define the resulting norm to be 0. So really we mean nor…”
Section: Definition 253mentioning
confidence: 99%
“…Other way to attack Question 6.1 is by large products of creature forcing (cf. [9,20,21]). Quite recently, A. Fischer, Goldstern, Kellner and Shelah [9] used this technique to prove that 5 cardinal invariants on the right of Cichoń's diagram are pairwise different.…”
Section: Discussion and Open Questionsmentioning
confidence: 99%
“…Goldstern, Kellner, and Shelah have studied cardinal coefficients of the form db,h Lc and bb,h aLc for bωω (with a different notation in their work) to provide the first examples of models where continuum many cardinal characteristics of the continuum are pairwise different . On the other hand, Brendle and Mejía investigated cardinals of the form bb,h Lc for bωω in relation with gap numbers for F σ ‐ideals .…”
Section: Notation and Preliminariesmentioning
confidence: 99%
See 1 more Smart Citation
“…It occurs that a strong version of halving from [4, Section 2.2] implies the properness of forcing notions of the type Q * ∞ (K, Σ). More on applications of halving can be found in Kellner and Shelah [2,3] and Ros lanowski and Shelah [5].…”
Section: Introductionmentioning
confidence: 99%