This conference focusses on several related interests of John: first order structures which are homogeneous in the sense of Fraïssé (or of more recent generalisations), and also ωcategorical structures in model theory; automorphism groups of such structures, and connections to other fields such as permutation group theory, semigroup theory, Ramsey theory and other aspects of combinatorics, topological dynamics; connections to set theory – related questions in combinatorial set theory, and permutation group methods in set theory.
The meeting is supported by the School of Mathematics at the University of Leeds and by the British Logic Colloquium.
Practical information
Registration
If you wish to attend, please submit the registration form.
Time and Venue
The meeting will take place in the School of Mathematics, University of Leeds, and will start around , and end around .
There will be a conference dinner on Monday September 11 (£34). If you wish to attend the social dinner, please say so in the registration form, and you will receive the payment instructions.
Travel & Accommodation
We have prebooked a limited number of single rooms at
Hotel Ibis (£52/night
incl. breakfast) for the nights of 10th and 11th
September. If you wish to stay at Ibis, please say so in
the registration form, and you will receive the payment
instructions. Payment is required before 7th August
2017. The reservation can be modified or cancelled before
7th August. No refund shall be possible after that date.
The deadline for booking at Ibis through the School has
closed.
For information on how to reach the School of Mathematics, please read the University instructions or see our location on Google Maps.
Speakers
 Manfred Droste (Leipzig)
 Mirna Dzamonja
(UEA) Some recent forcing
axioms
Recent results in set theory have made us reconsider the idea of forcing axioms, which for a while were considered as a finished subject. We shall discuss results of various authors, including some of our work joint with coworkers.

David Evans
(Imperial) Sparse graphs, EPPA
and Amenability
A class of finite structures has the Extension Property for Partial Automorphisms (EPPA) if every structure in the class can be embedded in a larger structure in the class having the property that every partial automorphism of the smaller structure extends to an automorphism of the larger structure. Where the class is the age of a countable homogeneous structure, this property has strong implications for the automorphism group of the structure: it is one of the main ingredients in applying the methods of Hodges, Hodkinson, Lascar and Shelah to prove the small index property and, by an observation of Kechris and Rosendal, it implies amenability.
I will describe some results about EPPA for certain classes of sparse graphs involved in the Hrushovski amalgamation constructions. There are negative results obtained from nonamenability and also positive results obtained from an extension of the Hodkinson  Otto method for proving EPPA. The latter has other applications and should be of independent interest.
This is joint work with Jan Hubička and Jaroslav Nešetřil.
 Thomas Forster (Cambridge)
 Andrew Glass (Cambridge)
 Bob Gray (UEA)

Dietrich Kuske
(Ilmenau) Locality of counting
logics
We introduce the logic FOCN(ℙ) which extends firstorder logic by counting and by numerical predicates from a set ℙ, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature.
We obtain a locality result showing that every FOCN(ℙ)formula can be transformed into a formula in Hanf normal form that is equivalent on all finite structures of degree at most d. A formula is in Hanf normal form if it is a Boolean combination of formulas describing the neighbourhood around its tuple of free variables and arithmetic sentences with predicates from ℙ over atomic statements describing the number of realisations of a type with a single centre. The transformation into Hanf normal form can be achieved in time elementary in d and the size of the input formula. From this locality result, we infer the following applications:
 The Hanflocality rank of firstorder formulas of bounded quantifier alternation depth only grows polynomially with the formula size.
 The model checking problem for the fragment FOC(ℙ) of FOCN(ℙ) on structures of bounded degree is fixedparameter tractable (with elementary parameter dependence).
 The query evaluation problem for fixed queries from FOC(ℙ) over fully dynamic databases of degree at most d can be solved efficiently: there is a dynamic algorithm that can enumerate the tuples in the query result with constant delay, and that allows to compute the size of the query result and to test if a given tuple belongs to the query result within constant time after every database update.
References
 Dietrich Kuske and Nicole Schweikardt. Firstorder logic with counting. In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, Reykjavik, Iceland, June 2023, 2017, pages 1–12. IEEE Computer Society, 2017.

James Mitchell (St
Andrews) Universal sequences for
groups and
semigroups
Oré's Theorem from 1951 states that every element of the symmetric group S_{X} on an infinite set X is a commutator. In other words, for any permutation p on an infinite set X, the equation p = a^{1}b^{1}ab has a solution in the symmetric group S_{X}. If w is any word over a finite alphabet, which is not a proper power of another word, and p is any permutation of an infinite set X, then Silberger, Droste, Dougherty, Mycielski, and Lyndon showed that p = w has a solution in permutations of X.
A universal sequence for a group or semigroup G is a sequence of words w_{1}, w_{2}, … such that for any sequence g_{1}, g_{2}, … ∈ G the equations w_i = g_i, i ∈ ℕ can be solved simultaneously in G. Galvin showed that the sequence {a^{1} (a^{i} ba^{i}) b^{1} (a^{i} b^{1} a^{i}) ba : i ∈ ℕ} is universal for the symmetric group S_{X} when X is infinite. On the other hand, if G is any countable group, then G has no universal sequences.
In this talk, I will discuss properties of universal sequences for some wellknown groups and semigroups.
Joint work with J. Hyde, J. Jonušas and Y. Péresse.

Jacob
Hilton The Cube Problem for Linear
Orders
In 1958, Sierpinski asked whether there is a linear order that is isomorphic to its cube (ordered lexicographically) but not to its square. This question was resolved in 2016 by Garrett Ervin. We will look at some of the ideas behind this result. As a warmup exercise, we invite the reader to find a nondense linear order that is isomorphic to its square.
 Carolyn Barker (Leeds)
 Milette TseelonRiis (Leeds)