Handbook of Mathematical Logic, Volume 90 (Studies in Logic and the Foundations of Mathematics)

HANDBOOK OF MATHEMATICAL LOGIC by Jon Barwise [Hardcover] 1165 pages ISBN: 072042285x The Handbook of Mathematical Logic is an attempt to share with the entire mathematical community some modern developments in logic. We have selected from the wealth of topics available some of those which deal with the basic concerns of the subject, or are particularly important for applications to other parts of mathematics, or both. Mathematical logic is traditionally divided into four parts: model theory, set theory, recursion theory and proof theory. We have followed this division, for lack of a better one, in arranging this book. It made the placement of chapters where there is interaction of several parts of logic a difficult matter, so the division should be taken with a grain of salt. Each of the four parts begins with a short guide to the chapters that follow. The first chapter or two in each part are introductory in scope. More advanced chapters follow, as do chapters on applied or applicable parts of mathematical logic. Each chapter is definitely written for someone who is not a specialist in the field in question. On the other hand, each chapter has its own intended audience which varies from chapter to chapter. In particular, there are some chapters which are not written for the general mathematician, but rather are aimed at logicians in one field by logicians in another. We hope that many mathematicians will pick up this book out of idle curiosity and leaf through it to get a feeling for what is going on in another part of mathematics. It is hard to imagine a mathematician who could spend ten minutes doing this without wanting to pursue a few chapters, and the introductory sections of others, in some detail. It is an opportunity that hasn’t existed before and is reason for the Handbook. -- Jon Barwise Front Cover Handbook of Mathematical Logic Copyright Page Table of Contents Foreword Contributors Part A: Model Theory Guide to Part A A.1. An introduction to first-order logic A.2. Fundamentals of model theory A.3. Ultraproducts for algebraists A.4. Model completeness A.5. Homogenous sets A.6. Infinitesimal analysis of curves and surfaces A.7. Admissible sets and infinitary logic A.8. Doctrines in categorical logic Part B: Set Theory Guide to Part B B.1. Axioms of set theory B.2. About the axiom of choice B.3. Combinatorics B.4. Forcing, John B.5. Constructibility B.6. Martin’s Axiom B.7. Consistency results in topology Part C: Recursion Theory Guide to Part C C.1. Elements of recursion theory C.2. Unsolvable problems C.3. Decidable theories C.4. Degrees of unsolvability: a survey of results C.6. Recursion in higher types C.7. An introduction to inductive definitions C.8. Descriptive set theory: Projective sets Part D: Proof Theory And Constructive Mathematics Guide To Part D Guide to Part D D.1. The incompleteness theorems D.2. Proof theory: Some applications of cut-elimination D.3. Herbrand’s Theorem and Gentzen’s notion of a direct proof D.4. Theories of finite type related to mathematical practice D.5. Aspects of constructive mathematics D.6. The logic of topoi D.7. The type free lambda calculus D.8. A mathematical incompleteness in Peano Arithmetic Author Index Subject Index Edited By Jon Barwise, With The Cooperation Of H. J. Keisler ... [et Al]. Includes Bibliographies And Indexes.