Computability Learning Seminar

Jonny Stephenson, Department of Pure Mathematics, University of Waterloo

"Degree Spectra"

Last week we saw that every countable ideal in the enumeration degrees is the co-spectrum of some structure. Now we will consider what sets of degrees are spectra of structures. We will see that the situation is quite different, and that there are a number of classes which cannot be the spectrum of any structure. In particular, no nontrivial countable union of enumeration upper cones can be the spectrum of any structure.

MC 5403