In the year 2014, both Peter Koepke and Philip Welch are celebrating their 60th birthdays, and this festive occasion is celebrated with this Festschrift in their honour containing scientific contributions of their students, collaborators, colleagues and friends which cover the various different research ares of logic in which Peter and Philip are active.

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies.

This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.

This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

This volume is both a tribute to Ulrich Felgner's research in algebra, logic, and set theory and a strong research contribution to these areas. Felgner's former students, friends and collaborators have contributed sixteen papers to this volume that highlight the unity of these three fields in the spirit of Ulrich Felgner's own research. The interested reader will find excellent original research surveys and papers that span the field from set theory without the axiom of choice via model-theoretic algebra to the mathematics of intonation.

"Foundations of the Formal Sciences" (FotFS) is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades.

The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software.

Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic.

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Games and Scales' (Part 1) and 'Suslin Cardinals, Partition Properties, and Homogeneity' (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory.

The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on 'Extensions of AD, models with choice', while Part VIII ('Other topics') collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe, CiE 2013, held in Milan, Italy, in July 2013.
The 48 revised papers presented together with 1 invited lecture and 2
tutorials were carefully reviewed and selected with an acceptance rate of under 31,7%. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing."

This book constitutes the refereed proceedings of the Turing Centenary Conference and the 8th Conference on Computability in Europe, CiE 2012, held in Cambridge, UK, in June 2012. The 53 revised papers presented together with 6 invited lectures were carefully reviewed and selected with an acceptance rate of under 29,8%. The CiE 2012 Turing Centenary Conference will be remembered as a historic event in the continuing development of the powerful explanatory role of computability across a wide spectrum of research areas. The papers presented at CiE 2012 represent the best of current research in the area, and forms a fitting tribute to the short but brilliant trajectory of Alan Mathison Turing. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing.

This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies.

This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this volume constitutes a selection of papers presented at the Internatonal Conference on Infinity in Logic and Computation, ILC 2007, held in Cape Town, South Africa, in November 2007.

The 7 revised papers presented together with 2 invited talks were carefully selected from 27 initial submissions during two rounds of reviewing and improvement. The papers address all aspects of infinity in automata theory, logic, computability and verification and focus on topics such as automata on infinite objects; combinatorics, cryptography and complexity; computability and complexity on the real numbers; infinite games and their connections to logic; logic, computability, and complexity in finitely presentable infinite structures; randomness and computability; transfinite computation; and verification of infinite state systems.

CiE 2009: Mathematical Theory and Computational Practice Heidelberg, Germany, July 19-24, 2009 After several years of research activity, the informal cooperation "C- putability in Europe" decided to take a more formal status at their meeting in Athens in June 2008: the Association for Computability in Europe was founded to promote the development, particularly in Europe, of computability-related science, ranging over mathematics, computer science, and applications in va- ous natural and engineering sciences such as physics and biology, including the promotion of the study of philosophy and history of computing as it relates to questionsofcomputability. As mentioned, this associationbuilds ontheinformal network of European scientists working on computability theory that had been supporting the conference series CiE-CS overthe years, and nowbecame its new home. The aims of the conference series remain unchanged: 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 on 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 proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15-20, 2008 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 on 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, computational learning. Applications are everywhere, especially, in algebra, analysisand geometry, or data types and p- gramming. Within CiE there is general recognition of the underlying relevance of computability to physics and a broad range of other sciences, providing as it does a basic analysis of the causal structure of dynamical systems. Thisvolume, Logic andTheory of Algorithms, istheproceedingsofthefourth in a series of conferences of CiE that was held at the University of Athens, June 15-20, 2

This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007.

The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions. Among them are papers corresponding to 12 plenary talks and papers of 8 special sessions entitled doing without turing machines: constructivism and formal topology, approaches to computational learning, real computation, computability and mathematical structure, complexity of algorithms and proofs, logic and new paradigms of computability, computational foundations of physics and biology, as well as a women in computability workshop.

This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and G del centenary: G del's legacy for computability.

CiE 2005: New Computational Paradigms http: //www. illc. uva. nl/CiE/ ThecooperationComputabilityinEurope (CiE)isaninformalEuropeannetwork covering computability in theoretical computer science and mathematical logic, ranging from application of novel approaches to computation to set-theoretic analysesofin?nitarycomputingmodels. Thecooperationconsistsofelevenmain nodesandincludesover400researchers;itiscoordinatedfromLeeds(UK). More information about CiE can be found in Barry Cooper's introductory paper to this volume (p. 1) and at http: //www. amsta. leeds. ac. uk/pure/staff/cooper/cie. html CiE 2005 was a conference on the special topic "New Computational Pa- digms" and was held in Amsterdam in June 2005. It was initiated by and served as a focus point for the informal cooperation CiE. The topic of "New Com- tational Paradigms" covers connections between computation and physical s- tems (e. g., quantum computation, neural nets, molecular computation) but also higher mathematical models of computation (e. g., in?nitary computation or real computation). Computability theory is central to large areas of theoretical computer science and mathematical logic. Traditionally, the computational model of the Turing machine (or mathematically equivalent models) has been used to reason about computation or computability. For general computability inquiries (with - bounded resources), the choice of the model of computation hardly matters (this fact is encapsulated in the so-called "Church-Turing thesis"); this could change as soon as questions of e?ciency are investigated.

Born in Calcutta in 1935, Bimal Krishna Matilal is regarded as one among the world's leading scholars of Indian Philosophy. His work can be considered as one of the most important bridges between Indian and Western logic. His untimely death in 1991 deprived the world of an outstanding thinker and philosopher. In January 2007, a conference was held in Matilal's home city Calcutta in his memory, bringing together logicians working on both Indian and Western logic. This thoroughly peer-reviewed volume contains a selection of the best papers; some represent Indian logic, others Western logic, and some continue Matilal's work of building bridges. The spirit of the 2007 Calcutta conference continues in the conference series ICLA, now run by the Association for Logic in India (ALI).

The research programme Semantics and Syntax: a Legacy of Alan Turing, held at the Isaac Newton Institute for the Mathematical Sciences in Cambrudge UK 9 January - July 2012, was one of the central activities of the Alan Turing Year 2012, the world-wide celebration of the life and work of the exceptional scientist Alan Mathison Turing (1912-1954). It had almost 200 visiting fellows and programme participants, as well as several hundred additional workshop participants, and was organised by Arnold Beckmann (Swansea), S. Barry Cooper (Leeds), Benedikt Lowe (Amsterdam & Hamburg), Elvira Mayordomo (Zaragoza), and Nigel Smart (Bristol). This volume documents the presentations that were given as part of the programme, which include the abstracts of the teaser talks given in the Seminar at the Isaac Newton Institute, and abstracts of the talks given at five of the seven workshops, as well as written versions of two open problem sessions."

This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.