Logic Colloquium 2005 Day 2
9:25: Theres wireless access in the large lecture theatre, so Ill take notes and upload comments occassionally through the day. At the moment, Phokion Kolaitis is giving his first short course lecture on constraint satisfaction problems. So far hes talking about examples of CSPs (graph colourings and 3-SAT are his first examples) and hes just looking now at homomorphisms of relational structures, and the Feder & Vardi claim (1993) that CSPs may be idenified with (or may be represented by) the problem of whether or not theres a homomorphism between two relational structures. (This bit is new to me, so Ill listen closely.)

11:20: Sergey Goncharov giving an invited lecture on Isomorphisms and Definable Relations on Computable Models. Its always struck me as weird that infinite ordinals have something to do with the characterisation of computable structures (where being computable is an essentially finitary notion in one sense  any computation process can be finitely described), but then, ordinal notations are finite too. Sergeys talk is about constucting interesting structures (boolean algebras, rings etc.) that are computable, but have the Scott Rank of ?1CK (thats big). This generalises some earlier results of Makkai (who showed that there were arithmetical structures of that rank) and Knight and Sheard (who showed that there were computable structures with that high a rank). Goncharovs results (proved by coding structures inside other structures) show how to construct familiar structures that are this complex. A related recent preprint is here.
