ℙmax variations for separating club guessing principles

Journal of Symbolic Logic 77 (2):532-544 (2012)
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Abstract

In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max 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 ω | . 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 ω | . In this paper we give an alternate proof of the second of these results, using Woodin's P max 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 P m a x machinery, is the use of condensation principles to build suitable iterations

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References found in this work

Canonical Models for ℵ1-Combinatorics.Saharon Shelah & Jindr̆ich Zapletal - 1999 - Annals of Pure and Applied Logic 98 (1-3):217-259.
Some Results About (+) Proved by Iterated Forcing.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):515-531.
The Canonical Function Game.Paul B. Larson - 2005 - Archive for Mathematical Logic 44 (7):817-827.

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