Past Logic Seminar

1 June 2007
15:15
Abstract
  Countable Borel equivalence relations arise naturally as orbit equivalence relations for countable groups. For each countable Borel equivalence relation E there is an infinitary sentence such that E is equivalent to the isomorphism relation on countable models of that sentence. For first order theories the question is open.  
4 May 2007
15:15
Andrew Duncan
Abstract
&nbsp; I shall describe some joint work with Vladimir Remeslennikov and Ilia Kazachkov. Partially commutative groups are groups given by a presentation determined by a graph: vertices are generators and edges define commutation relations. Divisbility and orthogonal systems are tools developed to study these groups. Using them we have descriptions of centralisers of subsets, a good understanding of the centraliser lattice in terms of the underlying graph and have made good progress towards classifying the universal theory of these groups as well as their automorphism groups. <!--#set var="updated_by" value="Laura Bentley" --> <!--#set var="maintainer_email" value="seminars@maths.ox.ac.uk"--> <!--#include virtual="/includes/footer.ssi" -->

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