Subject: set theory and its neighbours, 25/4, programme Set theory and its neighbours, 9 Dear Colleague This message is to give further information about the nineth one-day meeting in the series "Set theory and its neighbours", which will take place on on Wednesday 25th April 2001 at the London Mathematical Society building, De Morgan House, 57-58 Russell Square, London WC1. The meeting will start at 11am, when coffee will be available, and the first talk will be at 11.30. The last talk should finish at roughly 6pm. The speakers at the meeting will be: 11.30 Russell Barker (Oxford), Robinson-type relations and the relationship between the k-size and cardinality of finite structures Abstract: In this talk I will introduce the notions of L^k, the restriction of first order logic to k-variables, the k-size of a model and, two conjectures proposed by Anuj Dawar. Then I shall define define a special kind of relation which I shall call a Robinson-type relation and prove some results about these relations. I shall go on to give a translation between these relations and the set of L^3 theories and then use the earlier results to disprove Dawar's second conjecture. 12.30 Justin Moore (UEA), What makes the continuum $\aleph_2$? Abstract: I will discuss some of the past, present, and future of the statement "The continuum has size $\aleph_2$." 1.30 Lunch 2.30 Peter Koepke (Bonn), A new fine-structure theory for constructible inner models Abstract: We present a natural hierarchy for Godel's model L of constructible sets. The new hierarchy is immediately adequate for finestructural arguments. This will be demonstrated by a proof of Jensen's Covering Theorem for L. Further applications will be discussed. 3.30 Tea 4.00 Iain Stewart (Leicester) Finite model theory, computational complexity and program schemes Abstract: Finite model theory has strong connections with a number of topics within computer science. For example, assuming finite structure comes equipped with an ordering of its elements enables one to logically capture most mainstream complexity classes. However, one cannot always assume that one has access to an ordering of the elements of some finite structure: in database theory, for example, such orderings are almost always not available. In this talk I shall outline the concept of a program scheme, which is essentially a model for computing on arbitrary (not necessarily ordered) finite structures that sits somewhere between a Turing machine and a logical formula yet remains amenable to logical manipulation. I will show that many classes of program schemes have alternative formulations as previously-studied logics from finite model theory but that there are natural classes of program schemes giving rise to "new" logics with interesting properties. 5.00 Mirna Dzamonja (UEA), Combinatorial principles that follow from GCH-like cardinal arithmetic assumptions Abstract: We discuss various results showing that at certain cardinals diamond-like principles follow just from local GCH-like assumptions on cardinal arithmetic. More information, including slides from the talks will be available as we confirm it via the meetings' web-page: http://www.ucl.ac.uk/~ucahcjm/stn.html As ever, we hope to keep the meeting fairly relaxed, allowing plenty of opportunity for informal discussion. We welcome and encourage anyone to participate. You are very welcome simply to turn up on the day if you make a late decision. And we hope as many attendees as possible will be able to come to "DK" for informal discussions at the end of the talks section of the meeting. Please do tell anyone about the meeting who you think may be interested in it. And let us know if you would like to speak or have ideas for speakers at future meetings. We are very grateful to the LMS for allowing us to use De Morgan House as a venue. (De Morgan House is in the south-east corner of Russell Square, The nearest tube station is Russell Square, but De Morgan House is also only a short walk from Euston, Euston Square and Goodge Street stations. See the web-site for maps and similarly for directions to "DK".) Best regards, Charles