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March 2009 Decisive creatures and large continuum
Jakob Kellner, Saharon Shelah
J. Symbolic Logic 74(1): 73-104 (March 2009). DOI: 10.2178/jsl/1231082303

Abstract

For f,g∈ωωω let cf,g be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. cf,g is the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often.

It is consistent that cfε,gε=cfε,gεε for ℵ1 many pairwise different cardinals κε and suitable pairs (fε,gε).

For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision.

Citation

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Jakob Kellner. Saharon Shelah. "Decisive creatures and large continuum." J. Symbolic Logic 74 (1) 73 - 104, March 2009. https://doi.org/10.2178/jsl/1231082303

Information

Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1183.03035
MathSciNet: MR2499421
Digital Object Identifier: 10.2178/jsl/1231082303

Subjects:
Primary: 03E17 , 03E40

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 1 • March 2009
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