Logic Seminar-Spaces of orders

Time: Thursday, November 17, 11:00 am-12:00 noon

Place: Smith 120

Speaker:  Valentina Harizanov, GWU

Title: Spaces of orders

Abstract:  We investigate algebraic and computability-theoretic properties of orderable magmas. A magma is an algebraic structure with a single binary operation. A magma M is right-orderable (left-orderable) if there is a linear ordering of the domain of M, which is right-invariant (left-invariant) with respect to the magma operation. If M has a right order that is also a left order, then M is bi-orderable. A computable orderable magma does not necessarily have a computable order. There is a natural topology on the set of all (left, right, bi-) orders of M. These spaces are compact, and in some cases homeomorphic to the Cantor set.