The object of this paper is to explain a certain type of construction which occurs in priority proofs and illustrate it with two examples due to Lachlan and Harrington. The proofs in the examples are essentially the original proofs; our main contribution is to isolate the common part of these proofs. The key ideas in this common part are due to Lachlan; we include several improvements due to Harrington, Soare, Slaman, and the author.Our notation is fairly standard. If X is (...) an r.e. set, Xs is the finite set of elements enumerated in X before step s. if Ф is a recursive functional, Фs is the approximation to Ф at step s; it only queries the oracle about numbers xi and iless-than-or-equals, slantx; and right-pointing angle bracketx0,...,xk−1right-pointing angle bracket is an increasing function of each of its arguments. Sets are sometimes identified with their characteristic functions. Wj isthe jth r.e. set. Xc is the complement of X. (shrink)

§1. The origins of recursion theory. In dedicating a book to Steve Kleene, I referred to him as the person who made recursion theory into a theory. Recursion theory was begun by Kleene's teacher at Princeton, Alonzo Church, who first defined the class of recursive functions; first maintained that this class was the class of computable functions ; and first used this fact to solve negatively some classical problems on the existence of algorithms. However, it was Kleene who, in his (...) thesis and in his subsequent attempts to convince himself of Church's Thesis, developed a general theory of the behavior of the recursive functions. He continued to develop this theory and extend it to new situations throughout his mathematical career. Indeed, all of the research which he did had a close relationship to recursive functions.Church's Thesis arose in an accidental way. In his investigations of a system of logic which he had invented, Church became interested in a class of functions which he called the λ-definable functions. Initially, Church knew that the successor function and the addition function were λ-definable, but not much else. During 1932, Kleene gradually showed1 that this class of functions was quite extensive; and these results became an important part of his thesis 1935a. (shrink)

On April 26, 1995, the United States Supreme Court limited the reach of the preemption provision of ERISA in New York State Conference of Blue Cross & Blue Shield Plans v. Tavelers Insurance Co. ). In Travelers, the Supreme Court upheld the validity of a New York statute requiring hospitals to collect surcharges from patients covered by commercial insurers and requiring health maintenance organizations to pay a surcharge to the state's general fund that varies depending on the number of Medicaid-eligible (...) HMO members enrolled. Neither patients insured by Blue Cross/Blue Shield plans nor the plans themselves are similarly charged under the statute. Several commercial insurers and HMOs claimed the surcharges should be preempted under ERISA because they are levied on patients whose insurance or HMO membership premiums are purchased by an ERISA plan.The ERISA preemption clause means that federal regulation, or lack thereof, supersedes state regulation that is related to employee pension and benefit plans. This preemption clause prevents states from changing health care and benefit law for a significant portion of state residents. (shrink)

Guido de Ruggiero (1888-1948) was perhaps the greatest Italian intellectual historian in the twentieth century. He was a fierce champion of liberalism, an ardent opponent of Fascism, an insightful critic and interpreter of his contemporaries, and a formidable philosopher in his own right. Idealism & Experience: The Philosophy of Guido de Ruggiero comprises eight new critical essays, as well as English translations of five of de Ruggiero's most important shorter writings, which chart the development of his thought between 1914 and (...) 1946. Taken together, these essays reveal the range, richness and philosophical sophistication of de Ruggiero's ideas, enabling Anglophone readers to appreciate their enduring relevance in our own troubled times. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing his ideas (...) through lucid lecturing and writing. The present reference work, first published in 1832 and later revised, expanded and updated multiple times, made McCulloch considerable sums of money. His critical and analytical treatment of the data he had largely compiled himself made this much more than a mere book of facts. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing his ideas (...) through lucid lecturing and writing. The present work, first published in 1845, has been hailed as 'the first systematic account of the theory and policy of public finance'. After a general introductory chapter, the book discusses direct and indirect taxation, before considering national debt and how to deal with it. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing his ideas (...) through lucid lecturing and writing. The present reference work, first published in 1845, reflects McCulloch's extraordinarily wide reading across subjects relating to his field of expertise. Featuring sections on foundling hospitals and slavery, as well as money and prices, the bibliography is annotated throughout with McCulloch's frank assessments. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing his ideas (...) through lucid lecturing and writing. First published in 1825, this textbook was an expanded version of an article originally written in 1822 for the Encyclopaedia Britannica. Reissued here is the 1830 enlarged second edition. In Britain and America the work reached many students, and was translated into multiple European languages. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)

The object of this article is to examine the letter from which Plutarch quotes in the above passage from the twenty-eighth chapter of his life of Alexander; to attempt to prove, particularly by a comparison of the letter with the Sidypafifia sent in 319 B.C. by Polyperchon to the Greek cities, that it is a genuine part of Alexander's correspondence; and further to consider what light the letter, if genuine, throws upon the person of Alexander himself.

In his illuminating discussion of ‘the Caspian question’ Sir William Tarn, basing his case mainly on Aristotle, Meteorologica, 2. 1. 10 and Strabo, 11. 7. 4, argued that Alexander knew of the existence of the Aral Sea. Tarn's conclusion, however, was soon challenged by Professor Lionel Pearson, who disagreed in particular with Tarn's interpretation of the passage in Strabo. But, although he undoubtedly succeeds in showing that some of Tarn's arguments are not valid, Pearson fails, as it seems to me, (...) to disprove his main contention. Indeed, Pearson misunderstands the line of Strabo's argument and is led to propose an unnecessary emendation of the text. (shrink)

In an otherwise convincing article Mr. T. P. Wiseman argues that this passage ‘seems to mean that L. Memmius and Q. Pompeius were principes, i.e. outstanding orators, and that they were not among those who spoke in their own defence in 90 B.C.’. But he rightly refuses to believe that Cicero can have intended this, since, apart from other considerations, it is clear from Cicero's previous references to Memmius and Pompeius that he did not consider them to be outstanding orators.

The McNaughton Rules, which are used when someone pleads insanity at the time of a homicide, are out of date and unsatisfactory. Suggestions have been made about how the insanity defence can be reformulated. The preference of a defence of diminished responsibility means abandoning an ancient and humane principle of not convicting those who are so mentally disordered as not to be responsible for their actions. There is a need for Parliament to consider changes to the law both to prevent (...) the mentally disordered being sent to prison inappropriately, and because the Mental Health Act 1983 has not taken account of rare cases where an offender such as an epileptic might be found legally insane but not mentally disordered. (shrink)

The text of lines 39–40 is open to three main objections: stimulantem pectu Achilli cannot be construed in its context; to refer tuas to Persen would involvi difficult, though not unexampled, change of person; and thirdly, and most serious, it is scarcely possible to believe that Cornelia could appeal to a king of Macedon to testify to the soundness of her morals.

While Alexander is at Memphis an army arrives from Antipater including . It is a little surprising that Droysen's suggestion to read MevlSas for tevolras should have been accepted so readily by editors. We do at least hear fa Menoetas later as Berve remarks. He further points out lat Menidas does not elsewhere, so far as we know, command infantry.

Forty‐nine subjects judged the relevancy of sentence parts of a word problem (the Allsports problem). Patterns of subjects' judgments suggest three problem‐solving heuristics: a SETS heuristic, a TIME heuristic, and a QUESTION heuristic. Presentation of the question before the problem tends to suppress SETS and TIME heuristics. A computer program (ATTEND) is presented to simulate subjects' behavior on the Allsports problem. The program is context‐sensitive in that it can change a relevance judgment upon the acquisition of further information. Averaged subject (...) judgments and ATTEND judgments agree for 87% of the items. (shrink)

A lot of research has been done on the detection of mental workload using various bio-signals. Recently, deep learning has allowed for novel methods and results. A plethora of measurement modalities have proven to be valuable in this task, yet studies currently often only use a single modality to classify MWL. The goal of this research was to classify perceived mental workload using a deep neural network that flexibly makes use of multiple modalities, in order to allow for feature sharing (...) between modalities. To achieve this goal, an experiment was conducted in which MWL was simulated with the help of verbal logic puzzles. The puzzles came in five levels of difficulty and were presented in a random order. Participants had 1 h to solve as many puzzles as they could. Between puzzles, they gave a difficulty rating between 1 and 7, seven being the highest difficulty. Galvanic skin response, photoplethysmograms, functional near-infrared spectrograms and eye movements were collected simultaneously using LabStreamingLayer. Marker information from the puzzles was also streamed on LSL. We designed and evaluated a novel intermediate fusion multimodal DNN for the classification of PMWL using the aforementioned four modalities. Two main criteria that guided the design and implementation of our DNN are modularity and generalisability. We were able to classify PMWL within-level accurate on a seven-level workload scale using the aforementioned modalities. The model architecture allows for easy addition and removal of modalities without major structural implications because of the modular nature of the design. Furthermore, we showed that our neural network performed better when using multiple modalities, as opposed to a single modality. The dataset and code used in this paper are openly available. (shrink)