Abstract:
The author considers the conflict in Sierra Leone and the creation of the Special Court for Sierra Leone to bring to trial those who bear the greatest responsibility for the conflict. The provision of defence rights in post-war international proceedings is examined, in the International Military Tribunals, the International Criminal Tribunals and the more recent ‘hybrid’ tribunals in Kosovo, East Timor and Cambodia. Difficulties are identified with these structures. The considerations relevant to the creation of the Defence Office are discussed, together with its mandate, structure and operation. The delay in ensuring a fully operating office at the earliest stage due to budgetary restraints is identified as the key problem not to be repeated.

Abstract:
In gravitational instability models, there is a close relationship between most Lyman-alpha absorption and the matter density along the line of sight. Croft et al. (1997) have shown that it is possible to use this relationship with some additional assumptions (such as Gaussianity of the initial density) to recover the power spectrum of mass fluctuations, P(k), from QSO absorption spectra. The relative uniformity of the ionizing radiation background on the scales of interest is an additional assumption required by the technique. Here we examine the fluctuations in Lyman-alpha spectra caused if the ionizing background radiation is generated by discrete QSO sources. We present our results alongside the preliminary application of the P(k) recovery technique to the QSO Q1422+231. We find the ionizing background fluctuations to have an effect orders of magnitude smaller than the matter fluctuations at the scales on which we measure P(k) (lambda < 10 h^-1Mpc).

Abstract:
Suppose that \Delta, \Delta' are two buildings each arising from a semisimpe algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter diagram has no isolated nodes. We give conditions under which a partially defined injective chamber map, whose domain is the subcomplex of \Delta, generated by a nonempty open set of chambers, and whose codomain is \Delta', is guaranteed to extend to a unique injective chamber map. Related to this result is a local version of the Borel-Tits theorem on abstract homomorphisms of simple algebraic groups.

Abstract:
A new large-cardinal property is introduced which enables one to give a relative consistency proof of restricted versions of the reflection principles discussed by Tait in his essay "Constructing Cardinals from Below".

Abstract:
In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising this to the group of rational points of an absolutely quasi-simple algebraic group over a non-archimedean local field (the second method only achieves this on the additional hypothesis that the group is isotropic). The first method of argument involves demonstrating that, given any topological group $G$ which is totally disconnected, locally compact, $\sigma$-compact, locally topologically finitely generated, and has the property that no compact open subgroup has an infinite abelian continuous quotient, the group $G$ is topologically rigid in the previously described sense. Then the desired conclusion for the group of rational points of an absolutely quasi-simple algebraic group over a non-archimedean local field may be inferred as a special case. The other method of argument involves proving that any group of automorphisms of a regular locally finite building, which is closed in the compact-open topology and acts Weyl transitively on the building, has the topological rigidity property in question. This again yields the desired result in the case that the group is isotropic.

Abstract:
We present a proof of the following claim. Suppose that $n$ is an integer such that $n>1$ and that $k$ is any field. Suppose that $g$ is an element of $\mathrm{SL}(n,k)$ of infinite order. Then the set $\{h\in\mathrm{SL}(n,k)\mid $ is a free group of rank two$\}$ is a Zariski dense subset of $\mathrm{SL}(n,\bar{k})$ where $\bar{k}$ is an algebraic closure of $k$.

Abstract:
Building on previous work of Tait, Koellner, and myself exploring the question of which reflection principles are intrinsically justified on the basis of the iterative conception of set, we formulate a new reflection principle, which subsumes all previously known reflection principles which have been proposed as intrinsically justified and are also known to be consistent, and which is itself consistent relative to an $\omega$-Erd\"os cardinal. An open-ended family of strengthenings of this principle is tentatively proposed as exhausting everything that can be justified on the basis of the iterative conception of set.

Abstract:
We prove that if $G$ is a group of automorphisms of a regular locally finite building which is closed in the compact-open topology and acts Weyl transitively on the building, then $G$ admits just one Hausdorff locally compact $\sigma$-compact topology compatible with the group operations.