Computability learning seminar

Matthew Harrison-Trainor, Pure Mathematics University of Waterloo

“Omitting Partial Types and Hyperimmune Degrees - Part II”

We will show that hyperimmune degrees are able to omit non-principal partial types, and in fact are the only such types. By seeing that this proof can be carried out in RCA0, we will show that omitting partial types and the existence of hyperimmune degrees are equivalent over RCA0.