For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

This volume brings together academics from a variety of disciplines to discuss Collingwood's contributions to philosophy, aesthetics, philosophy of history, political philosophy and archaeological theory. It begins with a general survey of his contribution to history, politics and philosophy.

Since its conception nearly 20 years ago, Logic Programming - the idea of using logic as a programming language - has been developed to the point where it now plays an important role in areas such as database theory, artificial intelligence and software engineering. However, there are still many challenging research issues to be addressed and the UK branch of the Association for Logic Programming was set up to provide a forum where the flourishing research community could discuss important issues (...) of Logic Programming which were often by-passed at the large international conferences. This volume contains the twelve papers which were presented at the ALPUK's 3rd conference which was held in Edinburgh, 10-12 April 1991. The aim of the conference was to give a broad but detailed technical insight into the work currently being done in this field, both in the UK and by researchers as far afield as Canada and Bulgaria. The breadth of interest in this area of Computer Science is reflected in the range of the papers which cover - amongst other areas - massively parallel implementation, constraint logic programming, circuit modelling, algebraic proof of program properties, deductive databases, specialised editors and standardisation. The resulting volume gives a good overview of the current progress being made in the field and will be of interest to researchers and students of any aspects of logic programming, parallel computing or database techniques and management. (shrink)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there (...) was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

Part of the educational system in England has been geared towards the preparation of particular professions, while the identity and status of members of some professions have depended significantly on the general education they have received. Originally published in 1973, this volume explores the interaction between education and the professions. It also looks at the education of the main professions in sixteenth century England and at how twentieth century university teaching is a key profession for the training of new recruits (...) to other professions. (shrink)

Originally published in 1971, this volume examines the relationship between the history and sociology of education. History does not stand in isolation, but has much to draw from and contribute to, other disciplines. The methods and concepts of sociology, in particular, are exerting increasing influence on historical studies, especially the history of education. Since education is considered to be part of the social system, historians and sociologists have come to survey similar fields; yet each discipline appears to have its own (...) aims and methodology. (shrink)

Originally published in 1972, this book is concerned with education as part of a larger social history. Chapters include: The roots of Anglican supremacy in English education The Board schools of London The use of ecclesiastical records for the history of education Topographical resources: private and secondary education from the sixteenth to the twentieth century.

There is a common tradition in European education going back to the Middle Ages which long played a part in providing the curriculum of schools which catered both for the wealthy and for able sons of less well-to-do families. Originally published in 1974, this volume examines the relationship between education and society in the different countries of Europe from which differences in tradition and practice emerge. The countries discussed include: France, Germany, the former Soviet Union, Poland and Sweden.

A collection of eight lectures by renowned spiritual leader Swami Vivekananda, this volume presents a comprehensive introduction to Vedanta philosophy. Drawing on his personal experiences and insights, Vivekananda lays out a practical and accessible approach to spiritual seeking, emphasizing self-knowledge and direct experience. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and (...) possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.