2014 seminar talk: Orders on groups, their spaces, and complexity

Talk held by Valentina Harizanov (George Washington University, Washington, D.C., USA) at the KGRC seminar on 2014-03-06.


We investigate properties of orders on groups, which respect the algebraic structure. There is a natural topology on the (nonempty) set of such orders, and this space is compact even for a structure with a single binary operation (non necessarily a semigroup). We study the spaces as well as computability-theoretic complexity of orders on groups, both abelian and nonabelian. While not all computable orderable groups have computable orders, many familiar groups contain orders in every Turing degree above a specific degree.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.