Journal of Symbolic Logic

max variations for separating club guessing principles

Tetsuya Ishiu and Paul B. Larson

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Abstract

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

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

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1333566636

Digital Object Identifier
doi:10.2178/jsl/1333566636

Mathematical Reviews number (MathSciNet)
MR2963020

Zentralblatt MATH identifier
1251.03056

Subjects
Primary: 03E35: Consistency and independence results

Keywords
club guessing condensation ℛ_max

Citation

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. http://projecteuclid.org/euclid.jsl/1333566636.


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