ℛmax variations for separating club guessing principles
In his book on ℛmax , 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  while studying games of length ω₁. It was shown in  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.
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1333566636
Digital Object Identifier: doi:10.2178/jsl/1333566636
Zentralblatt MATH identifier: 06047775
Mathematical Reviews number (MathSciNet): MR2963020