June 2012 max variations for separating club guessing principles
Tetsuya Ishiu, Paul B. Larson
J. Symbolic Logic 77(2): 532-544 (June 2012). DOI: 10.2178/jsl/1333566636


In his book on ℛmax [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω₁. In this paper we employ one of the techniques from this book to produce ℛmax variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω₁. It was shown in [1] that the Continuum Hypothesis does not imply (+) and that (+) does not imply the existence of a club guessing sequence on ω₁. In this paper we give an alternate proof of the second of these results, using Woodin's ℛmax technology, showing that a strengthening of (+) does not imply a weakening of club guessing known as the Interval Hitting Principle. The main technique in this paper, in addition to the standard ℛmax machinery, is the use of condensation principles to build suitable iterations.


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Tetsuya Ishiu. Paul B. Larson. "max variations for separating club guessing principles." J. Symbolic Logic 77 (2) 532 - 544, June 2012. https://doi.org/10.2178/jsl/1333566636


Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1251.03056
MathSciNet: MR2963020
Digital Object Identifier: 10.2178/jsl/1333566636

Primary: 03E35

Keywords: club guessing , Condensation , ℛ_max

Rights: Copyright © 2012 Association for Symbolic Logic


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Vol.77 • No. 2 • June 2012
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