Computability learning seminar

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"Torsion-free groups: linear independence and computable categoricity"

We continue through Melnikov's survey paper on Computable  
Abelian Groups. We use the effective analysis of linear independence
(discussed before by Sam) to characterize computable categoricity. We
go through the proof that "Every computable torsion-free
abelian group of infinite rank has a presentation (computable) in
which linear independence is undecidable". It follows as a corollary
from this and an earlier proposition that "A computable torsion-free
abelian group is computably categorical iff its rank is finite".