We describe an algorithm that takes as input a complex sequence (un) given by a linear recurrence relation with polynomial coe cients along with initial values, and outputs a simple explicit upper bound (vn) such that |un| ≤ vn for all n. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of un. We discuss applications to the evaluation of power series with...

We present a comprehensive discussion of the consistency of the effective quantum field theory of a single Z2 symmetric scalar field. The theory is constructed from a bare Euclidean action which at a scale much greater than the particle’s mass is constrained only by the most basic requirements; stability, finiteness, analyticity, naturalness, and global symmetry. We prove to all orders in pertu...

The paper contributes to the theory of recursively presented (see Higman [22]) infinitely generated abelian groups with solvable word problem. Mal’cev [35] and independently Rabin [39] initiated the study of such groups in the early 1960’s. In the paper we develop a technique that we call iterated effective embeddings. The significance of our new technique is that it extends the iteration techn...

We investigate effective categoricity of computable Abelian p-groups A. We prove that all computably categorical Abelian p-groups are relatively computably categorical, that is, have computably enumerable Scott families of existential formulas. We investigate which computable Abelian p-groups are ∆02 categorical and relatively ∆ 0 2 categorical.