Computability Theory Learning Seminar

Xinyue (Cynthia) Xie & Layth Al-Hellawi, Department of Pure Mathematics, University of Waterloo

"Effectiveness Properties of Walker's Cancellation Theorem - Part I"

Walker's Cancellation Theorem is a result in group theory proven independently by Walker and Cohn in 1955. It states that if A is a finitely generated abelian group, and G and H are abelian groups such that A ⊕ G ≅ A ⊕ H, then G ≅ H. We will state and prove Walker's Cancellation Theorem with a focus on its computability theory aspects. Relevant group theory and computability theory concepts will be reviewed. This is Part I of a series of 4 talks where we present and build upon the work in Deveau's PhD thesis and examine Walker's Cancellation Theorem from a computability theory perspective.

MC 5417