Johanna N. Y. Franklin – författare

The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

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. The motto of CiE 2022 was “Revolutions and revelations in computability”. This alludes to the revolutionary developments we have seen in computability theory, starting with Turing's and Gödel's discoveries of the uncomputable and the unprovable and continuing to the present day with the advent of new computational paradigms such as quantum computing and bio-computing, which have dramatically changed our view of computability and revealed new insights into the multifarious nature of computation.

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. The motto of CiE 2022 was “Revolutions and revelations in computability”. This alludes to the revolutionary developments we have seen in computability theory, starting with Turing''s and Gödel''s discoveries of the uncomputable and the unprovable and continuing to the present day with the advent of new computational paradigms such as quantum computing and bio-computing, which have dramatically changed our view of computability and revealed new insights into the multifarious nature of computation.

This monograph introduces the reader to the increasingly popular topic of computable metric structure theory, a subject which unifies methods from effective analysis and computable algebra into one coherent framework. Computable structure theory had been constrained to the algebraic and discrete realms, but in the past 10 years or so, much work has been done in extending this topic to structures from analysis such as metric spaces, Banach spaces, and operator algebras. This book is the first comprehensive treatment of these basic results and discusses several challenging open problems that have arisen.  The book provides a foundation for the study of classic objects from functional analysis using tools from continuous model theory and computable structure theory.  It is largely self contained, though it is assumed that the reader is familiar with first-order logic. It should prove useful to students and researchers in continuous logic looking to familiarize themselves with computable structure theory as well as to researchers in the latter field looking to extend their work to structures from analysis. The discussion contains a large number of well-crafted examples and could provide the basis for a course or seminar in this area.