Computability Theory Learning Seminar

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part I"

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 semester in the computability seminar, we will be studying $\Pi^0_1$ classes from Cenzer \& Remmel's textbook. This week, we will begin by proving some basic properties and equivalent characterizations of $\Pi^0_1$ classes as the complement of a computable union of basic open sets, and as the set of points $x\in\omega^\omega$ satisfying $(\forall n<\omega)R(n,x)$ for some computable relation $R$. Time permitting, we will begin investigating different notions of boundedness in $\Pi^0_1$ classes.

MC 5403