This open access book provides insights from Indigenous higher degree research (HDR) students on supervision practices in an Australian context

This paper presents a syntax and semantics for Degree Neuter Relatives (DNRs) in Spanish, an unusual construction involving relative clause seemingly headed by gradable predicate the neuter determiner lo. I propose analysis of DNRs that avoids compositionality problems derived from sortal mismatches between degrees entities. In addition, suggest despite cross-linguistic rarity DNRs, it is no co...

We define the automorphism spectrum of a computable structure M, a measurement of the complexity of the symmetries of M, and prove that certain sets of Turing degrees can be realized as automorphism spectra, while certain others cannot.

Much of the work on Turing degrees may be formulated in terms of the embeddability of certain first-order structures in a structure whose universe is some set of degrees and whose relations, functions, and constants are natural degree-theoretic ones. Thus, for example, we know that if (P, ≤P ) is a partial ordering of cardinality at most א1 which is locally countable—each point has at most coun...

We consider the degree-diameter problem for Cayley graphs of dihedral groups. We find upper and lower bounds on the maximum number of vertices of such a graph with diameter 2 and degree d. We completely determine the asymptotic behaviour of this class of graphs by showing that both limits are asymptotically d/2.

Let G be a finite group and φ : V → W an equivariant morphism of finite dimensional G-modules. We say that φ is faithful if G acts faithfully on φ(V ). The covariant dimension of G is the minimum of the dimension of φ(V ) taken over all faithful φ. In this paper we investigate covariant dimension and are able to determine it for abelian groups and to obtain estimates for the symmetric and alter...