## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, November 24, 2022 — 10:30 AM EST

**Xinyue (Cynthia) Xie & Layth Al-Hellawi, Department of Pure Mathematics, University of Waterloo**

**"Effectiveness properties of the Walker's Cancellation Theorem - Part III"**

This is part III of a series of 4 talks in which we present and build upon the work in Deveau's PhD thesis and examine Walker's Cancellation Theorem from a computability theory perspective. In this talk, we will present a stronger version of Deveau's Theorem 4.1. Deveau's Theorem 4.1 states that given groups *E:= A ⊕ G = B ⊕ H*, where *A ≅ B* are cyclic with known generators, *G* and *H* are always computably isomorphic with some isomorphism *f*. Furthermore, if *A* and *B* are known to be finite, then f can be constructed uniformly in the indices of the groups. We will prove that regardless of the cardinality of *A* and *B*, the function that computes *f* is Turing reducible to the halting set. The notions of Turing reducibility, Turing degree and the Turing jump operator will be introduced.

MC 5417

Event tags

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.