Ulrich Berger - Böcker

At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites. Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory.

This book constitutes the proceedings of the 18th Conference on Computability in Europe, CiE 2022, in Swansea, UK, in July 2022. The 19 full papers together with 7 invited papers presented in this volume were carefully reviewed and selected from 41 submissions.

This book explains and exemplifies how SMEs can embrace the Smart Production approach and technologies in order to gain a beneficiary outcome. The book provides applied methods and obtained solutions in different branches and different sizes of SMEs, encompassing a broad survey of our markets and societies.

This book explains and exemplifies how SMEs can embrace the Smart Production approach and technologies in order to gain a beneficiary outcome. The book provides applied methods and obtained solutions in different branches and different sizes of SMEs, encompassing a broad survey of our markets and societies.

Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques concerned with those aspects. A key figure in this exciting development is the logician and mathematician Helmut Schwichtenberg to whom this volume is dedicated on the occasion of his 70th birthday and his turning emeritus. The volume contains 20 articles from leading experts about recent developments in Constructive set theory, Provably recursive functions, Program extraction, Theories of truth, Constructive mathematics, Classical vs. intuitionistic logic, Inductive definitions, and Continuous functionals and domains.

CiE 2006: Logical Approaches to Computational Barriers Swansea, Wales, June 30 - July 5, 2006 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti?c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory or relativity. Computations may be very general, depending upon the foundations of set theory; or very speci?c, using the combinatorics of ?nite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, and computational learning. Applications are everywhere, especially, in algebra, analysis and geometry, or data types and programming. This volume, Logical Approaches to Computational Barriers, is the proce- ings of the second in a series of conferences of CiE that was held at the Depa- ment of Computer Science, Swansea University, 30 June - 5 July, 2006.

Recent developments in computer science clearly show the need for a better theoretical foundation for some central issues. Methods and results from mathematical logic, in particular proof theory and model theory, are of great help here and will be used much more in future than previously. This book provides an excellent introduction to the interplay of mathematical logic and computer science. It contains extensively reworked versions of the lectures given at the 1997 Marktoberdorf Summer School by leading researchers in the field.Topics covered include: proof theory and specification of computation (J.-Y. Girard, D. Miller), complexity of proofs and programs (S. R. Buss, S. S. Wainer), computational content of proofs (H. Schwichtenberg), constructive type theory (P. Aczel, H. Barendregt, R. L. Constable), computational mathematics, (U. Martin), rewriting logic (J. Meseguer), and game semantics (S. Abramski).

Recent developments in computer science clearly show the need for a better theoretical foundation for some central issues. Methods and results from mathematical logic, in particular proof theory and model theory, are of great help here and will be used much more in future than previously. This book provides an excellent introduction to the interplay of mathematical logic and computer science. It contains extensively reworked versions of the lectures given at the 1997 Marktoberdorf Summer School by leading researchers in the field.Topics covered include: proof theory and specification of computation (J.-Y. Girard, D. Miller), complexity of proofs and programs (S. R. Buss, S. S. Wainer), computational content of proofs (H. Schwichtenberg), constructive type theory (P. Aczel, H. Barendregt, R. L. Constable), computational mathematics, (U. Martin), rewriting logic (J. Meseguer), and game semantics (S. Abramski).

Dieses Buch analysiert das Jahrhundertprojekt der europaweiten Vereinheitlichung des Massenzahlungsverkehrs durch das SEPA-Projekt (Single Euro Payment Area). Obwohl die Tragweite dieser Umgestaltung der europäischen Zahlungssysteme mit der Euro-Einführung vergleichbar ist, besteht darüber ein gravierendes Informationsdefizit im öffentlichen Diskurs. In diesem Buch findet sich eine kritische Analyse von SEPA aus wissenschaftlicher Perspektive.Im Mittelpunkt stehen Zahlungskartensysteme, da sie als zeitgemäße Zahlungsform in einer digitalisierten, globalisierten Welt von SEPA besonders betroffen sind. Die wichtigsten internationalen und nationalen Regulierungsinitiativen in diesem Bereich werden u.a. hinsichtlich der Interchange Fee einer eingehenden wissenschaftlichen Analyse unterzogen. Das Buch zeigt Handlungsalternativen für die Wirtschaftspolitik auf. Der derzeit verfolgte Ansatz läuft mangels einer soliden analytischen Fundierung Gefahr, die hochgesteckten Ziele und Erwartungen nicht erfüllen zu können.