Math Colloquium | Uncountable Linear Orders: A Brief Survey, Oct. 20

The Math Department colloquium series features Dr. Todd Eisworth  discussing "Uncountable Linear Orders: A Brief Survey" on Thursday, Oct. 20, at 4 p.m. in Morton Hall.

Eisworth is Associate Professor of Mathematics at Ohio University.

Abstract : Linearly ordered sets are simply-defined structures that are ubiquitous in mathematics. Countable linearly ordered sets are easy to understand: these all turn out to be isomorphic to some subset of the rationals, but what about uncountable linear ordered sets?  Some concrete things can be said, but one quickly runs into the independence phenomenon:  very often, answers to natural questions will turn out to be undecidable, neither provable nor refutable from the usual axioms that define the set-theoretic universe.  We will survey some results shedding light on the classification and potential behavior of uncountable linear orders, and finish by discussing some results obtained in research this past summer.