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)

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.

The present work sets out to discuss in three main steps the roots of the indeterministic paradigm for quantum mechanics as against a causal explanation of reality. The first step is to present the fundamental role played by non-local Fourier analysis in the Copenhagen paradigm. The second is to present wavelet local analysis, a recent formalism that will perhaps allow the development of a new causal paradigm for physics. The third is to present the Heisenberg-Bohr uncertainty relations as a direct (...) mathematical consequence of Fourier non-local analysis. Finally, experimental evidence violating these relations is presented. These results imply that the indeterministic approach has reached its limits. However, they can be explained within a causal framework allowing a more general mathematical formulation for uncertainty relations. (shrink)

XLRI, in association with a few Tata Group companies, established the XLRI-JRD Tata Foundation in Business Ethics in 1991 to mark their long-standing commitment and contribution to business ethics in India. The foundation seeks to address this by publicly affirming the urgent need for ethics in business and the need to bring about a conducive culture in which it can thrive.