Speaker: Valentina Harizanov, George Washington University

Title: Orders on structures

Abstract: We investigate topological and computability theoretic properties of left orders and bi-orders on groups. A group is left-orderable if there is a strict linear ordering of its domain, which is left-invariant with respect to the group operation. If the order is also right-invariant, then the group is bi-orderable. There is a natural topology on the set of all left orders, and this space is compact even for arbitrary (not necessarily associative) magmas. A group is computable if its domain is a computable set and its group operation is computable. A computable orderable group does not necessarily have a computable order. For familiar computable groups, we investigate algorithmic complexity of their orders measured by their Turing degrees.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491