A snapshot of logic

some recent results in mathematical logic

There will be a one day conference on 16 June, 2010 in London.

Venue: the new UEA London centre of the University of East Anglia .

The speakers will be:

Wilfrid Hodges , Oren Kolman , Dugald Macpherson , Lajos Soukup and Simon Thomas .

The conference will start at 10:30 and finish around 17:00, with the following programme:

10:30-11:00 welcome and coffee

11:00-11:45 Wilfrid Hodges, "A conjecture of Gaifman on relative categoricity"

Abstract: We form the language L(P) by adding a 1-ary relation symbol P to the language L. A complete theory T in L(P) is said to be relatively categorical if whenever A and B are models of T whose restrictions to P are isomorphic by an isomorphism f, then f extends to an isomorphism from A to B. In 1974 Gaifman conjectured that if T is relatively categorical then every model of the restriction of T to P can be extended to a model of T. In spite of work of Shelah I believe the conjecture is still open. Recent work of mine with Anatoly Yakovlev leads to a proof for abelian groups with distinguished subgroup, and the proof generalises, but I very much doubt that it will prove the whole conjecture. slides

11:45-12:30 Oren Kolman, "Duals vanishing from Black Boxes"

Abstract: Some prediction principles are provable in ordinary set theory. We provide an introductory discussion of some recent interactions of these with algebra and logic. slides

12:30-14:15 lunch break

14:15-15:00 Dugald Macpherson, "Vapnik-Cervonenkis density in some NIP theories"

Abstract: slides

15:00-15:30 tea

15:30-16:15 Lajos Soukup, "Cardinality spectrums and pcf theory" slides

16:15-17:00 Simon Thomas, "Ramsey Cardinals and the HNN Embedding Theorem"

Abstract: The Higman-Neumann-Neumann Embedding Theorem states that any countable group G can be embedded into a 2-generator group K. In the standard proof of this classical theorem, the construction of the group K involves an enumeration of a set of generators of the group G; and it is clear that the isomorphism type of K usually depends upon both the generating set and the particular enumeration that is used. In this talk, I will consider the question of whether there is a more uniform construction with the property that the isomorphism type of K only depends upon the isomorphism type of G. slides

17:00 discussion and close.


We aim to keep the meeting fairly relaxed, allowing plenty of opportunity for informal discussion. We welcome and encourage anyone to participate. Please do tell anyone about the meeting who you think may be interested in it. If you intend to come, it would be useful for catering purposes if you email one of the organisers to let us know, but you are also very welcome simply to turn up on the day if you make a late decision.

There is no registration fee for the meeting and coffee and tea during the breaks are provided.

Organisers: Mirna Dzamonja m.dzamonja at uea.ac.uk and David Evans d.evans at uea.ac.uk

The conference is entirely supported by the University of East Anglia.