Computability Learning Seminar

Jonny Stephenson, Department of Pure Mathematics, University of Waterloo

"Sets which are not the spectrum of any structure"

We continue our analysis of spectra, and show that no spectrum can be the Turing-upward closure of an F_sigma family of reals, unless that  upward closure is already an enumeration upper cone. We will see that, as in the case of the "no two cones" theorem, the key to the proof is to construct a suitably generic copy of a structure to see that it cannot possibly have the indicated spectrum.

MC 5403