In his book on ℙmax [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 ℙmax 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 ω1. In this paper we give an alternate proof of the second of these results, using Woodin's ℙmax 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 ℙmax machinery, is the use of condensation principles to build suitable iterations.
