From permutation groups to model theory

I cannot resist a conference with a title like this! But in this case, there is another very important reason to attend.

In the mid-1970s, when I began being interested in infinite permutation groups (I had been a strictly finite person before that point), I soon came to realise that I would need to know some model theory. As I have told elsewhere on this blog (for example, here, here and here), I learned it by volunteering to give the second-year lectures on logic in Oxford. I was also helped by Graham Higman’s advanced class on the Ryll-Nardzewski theorem (also proved at the same time by Engeler and by Svenonius), which says (in one formulation) that a countable first-order structure is determined up to uniqueness by the first-order sentences it satisfies together with the condition of countability if and only if its automorphism group is what is now called oligomorphic. In other words, in this situation at least, (first-order) axiomatisability is equivalent to a very high degree of symmetry. This is one of my very favourite theorems in mathematics.

Soon afterwards, Dugald Macpherson (whose undergraduate degree in Oxford was in Mathematics and Philosophy – he had been my student at Merton College) began his DPhil under my supervision. As with many of my students, he taught me much more than he learned from me; he contributed more than anyone else to the study of oligomorphic permutation groups, and has subsequently done much more in model theory and permutation groups, including work on o-minimality and on simplicity of automorphism groups.

Now Dugald is 60, and the occasion is being celebrated by a conference at the International Centre for Mathematical Sciences in Edinburgh, from 17 to 21 September this year. I will certainly be there. It looks like a super conference; many of the things I talk about here will be discussed at the meeting. The invited speakers are Peter Cameron (St Andrews), Zoé Chatzidakis (ENS, Paris), Gregory Cherlin (Rutgers), Richard Elwes (Leeds), David Evans (Imperial College), Ehud Hrushovski (Oxford), Martin Liebeck (Imperial College), Dugald Macpherson (Leeds), Angus Macintyre (QMUL), Peter Neumann (Oxford), Jaroslav Nešetřil (Charles Uni., Prague), Anand Pillay (Notre Dame), Cheryl Praeger (Uni. West. Australia), Charlie Steinhorn (Vassar), Pierre Simon (Berkeley), Slawomir Solecki (Cornell), Katrin Tent (Münster), Simon Thomas (Rutgers), John Truss (Leeds).

The web page for the conference is at http://www.icms.org.uk/permutationgroups.php. Space is limited, and registration closes on 8 June (or maybe 9 June), so apply now! There is a registration form available from the web page.

See you there!

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About Peter Cameron

I count all the things that need to be counted.
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