Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo
"Effectively closed sets -- Part II"
An effectively closed set (or $\Pi^0_1$ class) in Baire space $\omega^\omega$ is the set $[T]$ of infinite branches through a computable tree $T$. This week, we will discuss different notions of boundedness in $\Pi^0_1$ classes, the computability properties of the tree $T_P$ of initial segments of a $\Pi^0_1$ class $P$, and the computability properties of members of $\Pi^0_1$ classes. Time permitting, we will begin discussing some applications of effectively closed sets.