TY - JOUR
T1 - Creature forcing and large continuum
T2 - The joy of halving
AU - Kellner, Jakob
AU - Shelah, Saharon
PY - 2012/2
Y1 - 2012/2
N2 - 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, for continuum many pairwise different cardinals κ ε and suitable pairs (f ε, g ε. For the proof we introduce a new mixed-limit creature forcing construction.
AB - 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, for continuum many pairwise different cardinals κ ε and suitable pairs (f ε, g ε. For the proof we introduce a new mixed-limit creature forcing construction.
KW - Cardinal Characteristics
KW - Creature forcing
KW - Large Continuum
KW - Slaloms
UR - http://www.scopus.com/inward/record.url?scp=84855190520&partnerID=8YFLogxK
U2 - 10.1007/s00153-011-0253-8
DO - 10.1007/s00153-011-0253-8
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AN - SCOPUS:84855190520
SN - 0933-5846
VL - 51
SP - 49
EP - 70
JO - Archive for Mathematical Logic
JF - Archive for Mathematical Logic
IS - 1-2
ER -