We introduce the notion of a degree spectrum of a complete theory to be the set of Turing degrees that contain a copy of some model of the theory. We generate examples showing that not all degree spectra of theories are degree spectra of structures and vice-versa. To this end, we give a new necessary condition on the degree spectrum of a structure, specifically showing that the set of PA degree...

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the evdegree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we d...

We introduce a natural strengthening of prompt simplicity which we call strong promptness, and study its relationship with existing lowness classes. This notion provides a ≤wtt version of superlow cuppability. We show that every strongly prompt c.e. set is superlow cuppable. Unfortunately, strong promptness is not a Turing degree notion, and so cannot characterize the sets which are superlow cu...

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...