Journal of Symbolic Logic

max variations for separating club guessing principles

Tetsuya Ishiu and Paul B. Larson

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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.

Article information

J. Symbolic Logic, Volume 77, Issue 2 (2012), 532-544.

First available in Project Euclid: 4 April 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results

club guessing condensation ℛ_max


Ishiu, Tetsuya; Larson, Paul B. ℛ max variations for separating club guessing principles. J. Symbolic Logic 77 (2012), no. 2, 532--544. doi:10.2178/jsl/1333566636.

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