The meeting will run from friday evening 27/iii until sunday
afternoon 29/iii in Meeting Room 4 in the Centre for Mathematical
Sciences.

(Most)
people from outside Cambridge will be accommodated in Churchill
College. Please present yourself at the Porters' Lodge to be given a
packet containing instructions and things like keys-to-your-room. Two
UEA people (needing twin rooms) will be put up in significantly more
spacious guest rooms in Clare Hall. Again, go to the Porters'
Lodge.

The home team consists of Zachiri Mackenzie (who is cunning enough to not have a mobile), Vu Dang (who isn't: 07703735217) and tf (ditto: 07887701562)

The weekend will be devoted to a set of minicourses. The idea is that the minicourses will run concurrently, each with three or four lectures spread over three days.

**Lecture One**: The basic Fraissé theory, with
examples. Definition of the age of a structure, amalgamation class and
homogeneous structure, back-and-forth method. Fraissé's Theorem. As
basic examples, linear orders, coloured linear orders, the random
graph, the generic partial order.

**Lecture Two**: The above theory will be illustrated with regard
to work currently in progress (with Jenkinson and Seidel, former
students). This concerns the classification of the countable
homogeneous multipartite graphs. The work follows some of the features
of an earlier paper (Torrezão and Truss) where the countable
homogenous coloured partial orders were classified. We start with the
bipartite case, where the classification is known (Goldstern,
Grossberg, Kojman), where there are 5 types, empty, complete, perfect
matching and its complement, and generic. Then we consider the
tripartite and quadripartite cases, and discuss how the overall
classification is handled. There are some interesting and quite
complicated features.

**Lecture Three**: Whereas in Lecture 2 we examined structures
where the standard Fraissé theory applies, there have been a number of
modifications using essentially the same ideas. The most famous
methods are due to Hrushovski, but in this lecture I shall mention a
construction of a certain digraph by David Evans, and extensions of
this by myself and Daniela Amato. The key idea is once more that we
are seeking to construct, or possibly describe, certain (countably)
infinite structures, in this case digraphs, which have some reasonable
amount of symmetry, and we do this by means of a series of
approximations. In the case of homogeneous structures, the
approximations are actually finite, but in the modifications they may
only be finite in some weaker sense (finitely generated for
instance). An important feature is that there must only be countably
many structures which are allowed approximations, to ensure that the
construction terminates in countably many steps.

A global problem in the history of logic is why progress between Aristotle and the nineteenth century was so painfully slow. Among various likely reasons, one is that several ideas we take for granted today were in conflict with basic and often unspoken principles of traditional logic. I trace this for three ideas.

**Lecture One**: Relational logic, which was in conflict with the principle of
Top-Level Processing. Evidence: Ibn Sina 'Qiyas', Ockham, Leibniz, Frege
'Begriffsschrift'.

**Lecture Two**: Discharge of assumptions, which was in conflict with the
principle of Local Formalising. Evidence: Ibn Sina 'Qiyas', Port-Royal Logic,
Frege 'Grundlagen der Geometrie', Lukasiewicz.

**Lecture Three**: Type-theoretic semantics, which was in conflict with the
Aristotle-Porphyry theory of ideas. Evidence: Ammonius, Ibn Sina 'Ibara',
Wallis, Frege 'Grundlagen der Arithmetik' and 'Grundgesetze'.

I hope to be able to hand out translations of the relevant essays of
Ibn Sina) . Meanwhile here is the link to
the lecture notes and here is the link to
the relevant texts.

Slots

At this stage the exact timings are undetermined. Friday we can't really start much before 6, because i have to get back from Norwich. We will have lunch and dinner on saturday on site. The only thing that is

Friday

1800

then dinner

Then a talk at 20:00 from Peter Smith

Saturday

0900

1045

1200

1430

1615

1800

then dinner

Sunday

0900

1045

1200

1430

DPMMS front page.