The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, and… (More)

The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers. A description of the alogorithm and its programming is given here… (More)

In the past few years there has been a resurgence of interest in discrete models of computation that are allowed to act transfinitely. Such conceptual machines act in simple steps or stages, and have… (More)

In a series of recent papers, 1 Hartry Field has proposed a novel class of solutions to the semantic paradoxes, and argued that the new solutions are 'revenge-immune'. He has argued, in particular,… (More)

Turing’s seminal 1936 paper ‘On computable numbers, with an application to the Entscheidungsproblem’ is remarkable in several ways: firstly he had set out to solve Hilbert’s decision problem of the… (More)

We give a proof of a theorem of Jensen and Zeman on the existence of a global sequence in the Core Model below a measurable cardinal κ of Mitchell order (oM (κ)) equal to κ, and use it to prove the… (More)

We review two of Alan Turing’s chief publications in mathematical logic: the classic 1936 paper On Computable Numbers [9] and the less well known paper Systems of Logic based on Ordinals [10]. Whilst… (More)