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...

1 ABSTRACT Arikan 2] has proved a lower bound on the th moment of the number of guesses required to determine X given Y; which uses the R enyi entropy of order 1=(1+): We give a randomized improvement of Arikan's lower bound. Baumer 5] has proved the relationship 1 1 ? 2 ?H(XjY) ; between 1 |the probability of error if the plaintext X is to be estimated (with one guess allowed) given the cipher...