Displaying similar documents to “Iteration of λ -complete forcing notions not collapsing λ + .”

On the open-open game

Peg Daniels, Kenneth Kunen, Haoxuan Zhou (1994)

Fundamenta Mathematicae


We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which...