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The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.
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is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes.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.
Ernst Specker has made decisive contributions towards shaping direc tions in topology, algebra, mathematical logic, combinatorics and algorith mic over the last 40 years. We have derived great pleasure from marking his seventieth birthday by editing the majority of his scientific publications, and thus making his work available in a unified form to the mathematical community. In order to convey an idea of the richness of his personality, we have also included one of his sermons. Of course, the publication of these Selecta can pay tribute only to the writings of Ernst Specker. It cannot adequately express his originality and wisdom as a person nor the fascination he exercises over his students, colleagues and friends. We can do no better than to quote from Hao Wang in the 'Festschrift' Logic and Algorithmic I: Specker was ill for an extended period before completing his formal education. He had the leisure to think over many things. This experi ence may have helped cultivating his superiority as a person. In terms of traditional Chinese categories, I would say there is a taoist trait in him in the sense of being more detached, less competitive, and more under standing. I believe he has a better sense of what is important in life and arranges his life better than most logicians. We are grateful to Birkhauser Verlag for the production of this Selecta volume. Our special thanks go to Jonas Meon for sharing with us his intimate knowledge of his friend Ernst Specker.
This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.
LOGIC COLLOQUIUM '69
Contains survey papers on some of the mainstream areas of set theory and research. This book covers topics such as Omega-logic, applications of set theory to lattice theory and Boolean algebras, real-valued measurable cardinals, complexity of sets and relations in continuum theory, weak subsystems of axiomatic set theory, and more.
This book constitutes the refereed proceedings of the 15th Conference on Computability in Europe, CiE 2019, held in Durham, UK, in July 2019. The 20 revised full papers presented were carefully reviewed and selected from 35 submissions. In addition, this volume includes 7 invited papers. The conference CiE 2018 had the following six special sessions: computational neuroscience, history and philosophy of computing, lowness notions in computability, probabilistic programming and higher-order computation, smoothed and probabilistic analysis of algorithms, and transnite computations.