章节目录
Foreword Contributors PART A: MODEL THEORY Guide to Part A A.l. An introduction to first-order logic, Jon Barwise A.2. Fundamentals of model theory, H. Jerome Keisler A.3. Ultraproducts for algebraists, Paul C. Eklof A.4. Model completeness, Angus Macintyre A.5. Homogenous sets, Michael Morley A.6. Infinitesimal analysis of curves and surfaces, K. D. Stroyan A.7. Admissible sets and infinitary logic, M. Makkai A.8. Doctrinesincategoricallogic,A.Kock andG.E.Reyes PART B: SET THEORY Guide to Part B B.1. Axioms of set theory, J.R.Shoenfield B.2. About the axiom of choice, ThomasJ. Jech B.3. Combinatorics, Kenneth Kunen B.4. Forcing,JohnP.Burgess B.5. Constructibility, Keith J. Deulin B.6. Martin’s Axiom, Mary Ellen Rudin B.7. Consistency results in topology, I. Juhasrz PART C: RECURSION THEORY Guide to Part C C.l. Elements of recursion theory, Herbert B. Enderton C.2. Unsolvable problems. Martin Davis C.3. Decidable theories. Michael O. Rabin C.4. Degrees of unsolvability: a survey of results. Stephen G. Simpson C.5. a-recursion theory. Richard A. Shore C.6. Recursion in higher types. Alexander Kechris and Yiannis N. Moschovakis C.7. An introduction to inductive definitions, Peter Aczel C.8. Descriptive set theory: Projective sets, Donald A. Martin PART D: PROOF THEORY AND CONSTRUCTIVE MATHEMATICS Guide to Part D D.l. The incompleteness theorems. C. Smorynski D.2. Proof theory: Some applications of cut-elimination, Helmut Schwichtenberg D.3. Herbrand’s Theorem and Gentzen’s notion of a direct proof, Richard Statman D.4. Theories of finite type related to mathematical practice, Solomon Feferman D.5. Aspects of constructive mathematics. A. S. Troelstra D.6. The logic of topoi, Michael P. Fourman D.7. The type free lambda calculus, Henk Barendregt D.8. A mathematical incompleteness in Peano Arithmetic, Jeff Paris and Leo Harrington Author Index Subject Index
内容简介
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 mathemat- ical 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 the reason for the Handbook.
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