## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, September 17, 2014 — 3:40 PM EDT

We say a structure is computable (or computably presented) if it has domain the natural numbers, and if all functions, relations and constants are uniformly computable. This definition is not isomorphism invariant. We can ask: between two computable copies of a given structure, what is this simplest isomorphism that must exist? For example, between any two computable copies of the rationals, there always exists a computableisomorphism, since the usual back-and-forth isomorphism can be found effectively. On the other hand, the difficulty of computing an isomorphism between two computable copies of (N, ¡) is exactly that of the halting set, since we need to answer the single- quantifier questions of which element is least, next, etc. In this talk, we present what is known about Turing degrees that arise as degrees of isomorphisms for computable structures.

Please note time.

Location

M3 - Mathematics 3

4206

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1