Jech uses the following forcing notion to force GCH. For each $\alpha$, let $P_\alpha$ be the notion of forcing that collapses $\beth_{\alpha+1}$ to $\beth_\alpha^+$. $P$ is then the Easton product of these notions. For simplicity, we'll assume there are no inaccessible cardinals. Let $P^{< \alph...

Suppose $(X,\tau)$ is a topological space, $B$ is a base for $\tau$, and $U\in \tau$ is an open set. Consider the following two strategies for writing $U$ as a union of elements of $B$: We have $U=\bigcup\{V\in B: V\subseteq U\}$. For each $u\in U$ pick some $V_u\in B$ with $u\in V_u\subseteq U...

A set $X\subseteq\omega^\omega$ is unravelable iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to win...