Club Guessing and the Universal Models

Club Guessing and the Universal Models

We survey the use of club guessing and other pcf constructs in the context of showing that a given partially ordered class of objects does not have a largest, or a universal element. 1

Club-guessing, stationary reflection, and coloring theorems

We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals.

Guessing Clubs in the Generalized Club Filter

We present principles for guessing clubs in the generalized club filter on Pκλ. These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflecti...

The comparison of various club guessing principles

Pmax VARIATIONS FOR SEPARATING CLUB GUESSING PRINCIPLES

In his book on Pmax [6], 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 [3] while s...