This book offers a self-contained exposition of the theory of computability in a higher-order context where computable operations may themselves be passed as arguments to other computable operations. This book offers a self-contained exposition of the theory of com... Lees meer.

This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra analysis and topology. These include effective versions of Borel equivalence Borel reducibility and Borel dete... Lees meer.

This book constitutes the refereed proceedings of the 19th International Conference on Unity of Logic and Computation CiE 2023 held in Batumi Georgia during July 24 28 2023. The 23 full papers and 13 invited papers included in this book were carefully reviewed and... Lees meer.

Ranging from Alan Turing s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. Ranging from Alan Turing s semi... Lees meer.

Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing s seminal work in the 1930s. This was motivated by questions such as. which real numbers and real number functions are computable and which mathematical task... Lees meer.

Computability theory is at the heart of theoretical computer science. Yet ironically many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result many texts on computability theory stri... Lees meer.

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... Lees meer.

This survey of computability theory offers the techniques and tools that computer scientists as well as mathematicians and philosophers studying the mathematical foundations of computing need to mathematically analyze computational processes and investigate the theore... Lees meer.

This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning. Among the topics dealt with are. classical analysis Hilbert and Banach spaces bounded and unbounded linear operators eigen... Lees meer.

The ability to reason and think in a logical manner forms the basis of learning for most mathematics computer science philosophy and logic students. Based on the author s teaching notes at the University of Maryland and aimed at a broad audience this text covers the... Lees meer.

Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include. Can we prove th... Lees meer.

This highly readable and intuitive introduction to computability theory contains a great many background discussions which introduce the reader to the researched history and philosophical aspects of recursion theory and logic. This book is perfectly suited for class wor... Lees meer.

The interplay between computability and randomness has been an active area of research in recent years reflected by ample funding in the USA numerous workshops and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are c... Lees meer.

This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe CiE 2016 held in Paris France in June July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected fro... Lees meer.

The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. This volume provides a picture of current ideas and methods in the ongoing investigations into the pure mathematical fo... Lees meer.