Computability Seminar MSRI program on DDC-Effective ringed spaces and Turing degrees of isomorphism types

Organizer: V. Harizanov

For link contact [email protected]

Friday, September 18, 12:00-1:00 on Zoom

Speaker:  Wesley Calvert SIU

Title: Effective ringed spaces and Turing degrees of isomorphism types
 

Abstract:  The Turing degree spectrum of a countable structure A is the set of all Turing degrees of isomorphic copies of A.  The Turing degree of the isomorphism type of A is the least degree in this spectrum, if there is a least degree.  Frequently one can prove that, for a given class K of structures (e.g., the class of fields), for any Turing degree d there is an element of K whose isomorphism type has degree d.  Frequently this result is established by finding that K has certain combinatorial properties.  Here we show that this universality property holds for various classes of ringed spaces: unions of subvarieties of a fixed variety, unions of arbitrary ringed spaces, and schemes.