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Perspectives • tn Mathematical Logic 0-Group: R. 0. Gandy H. Hermes A. Levy G. H. Muller G. E. Sacks D. S. Scott 0-Bibliography of Mathematical Logic Edited by Gert H. Muller In Collaboration with Wolfgang Lenski VolumeV Set Theory Andreas R. Blass (Editor) Springer-Verlag Berlin Heidelberg GmbH Gert H. Muller Wolfgang Lenski Mathematisches Institut, UniversiUit Heidelberg Im Neuenheimer Feld 288, D-6900 Heidelberg Andreas R. Blass Department of Mathematics University of Michigan Ann Arbor, MI 48109 U.S.A. The series Perspectives in Mathematical Logic is edited by the .Q-Group of the Heidelberger Akademie der Wissenschaften. The Group initially received a generous grant (1970-1973) from the Stiftung Volkswagenwerk and since 1974 its work has been incorporated into the general scientific program of the Heidelberger Akademie der Wissenschaften (Math. Naturwiss. Klasse). ISBN 978-3-662-09066-4 ISBN 978-3-662-09064-0 (eBook) DOI 10.1007/978-3-662-09064-0 Library of Congress Cataloging in Publication Data [Omega]-bibliography of mathematical logic. (Perspectives in mathematical logic) Includes indexes. Contents: v. 1. Classical logic I Wolfgang Rautenberg, ed. - v. 2. Non-classical logics I Wolfgang Rautenberg, ed.- v. 3. Model theory I Heinz-Dieter Ebbinghaus, ed. [etc.] 1. Logic, Symbolic and mathematical-Bibliography. I. Miiller, G. H. (Gert Heinz), 1923 - II. Lenski, Wolfgang, 1952 -.III. Title: Bibliography of mathematical logic. IV. Series. Z6654.M26047 1987 [QA9) 016.5113 86-31426 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under§ 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1987 Originally published by Springer-Verlag Berlin Heidelberg New York in 1987 Softcover reprint of the hardcover 1st edition 1987 214113140-543210 Dedicated to Alonzo Church whose bibliographic work for the Journal of Symbolic Logic was a milestone in the development of modern logic. Table of Contents Preface ... . IX Introduction . XV User's Guide XXXI Q-Classification Scheme . XXXIX Subject Index . . . . . . . 1 Combinatorial set theory E05. 3 Relations and orderings . . . . . . . . . . E07. 27 Other classical set theory. . ~ . . . . . . . E20. 48 Axiom of choice and related propositions E25. 58 Ordinal and cardinal numbers . . . . . . E10. 74 Continuum hypothesis and Martin's axiom E50. 89 Large cardinals . . . . . . . . . . . . . . . . E55. . 108 Determinacy and related principles which contradict the axiom of choice . . . . . . . . . . E60. . 122 Other hypotheses and axioms . . . . . . . . . . . . . E65. . 128 Consistency and independence results . . . . . . . . E35. . 134 Other aspects of forcing and Boolean-valued models E40. . 154 Constructibility, ordinal definability and related notions E45. . 161 Other notions of set-theoretic definability E47. . 173 Descriptive set theory . . . E15. . 177 Applications .. . . . . . . . . . . . . E75. . 197 Set-theoretic model theory. . . . . . Part of C55. . 233 Models of arithmetic and set theory. Part of C62. . 242 Axiomatics of classical set theory and its fragments . . . . . E30. . 252 Nonclassical and second-order set theories ..... E70. . 267 Categorical logic, topoi Part of G30 . 284 Fuzzy sets ..... . E72. . 293 Proceedings . . . . . . . E97. . 304 Textbooks, surveys . . . E98. . 305 None of the above or uncertain, but in this section E99. . 311 Author Index . . 313 Source Index . 691 Journals . . 693 Series ..... . 719 Proceedings . . 723 Collection volumes . 744 Publishers . . . . . . 752 VIII Table of Contents Miscellaneous Indexes . . 761 External classifications ................... . . 763 Alphabetization and alternative spellings of author names . . 787 International vehicle codes . . . . . 789 Transliteration scheme for Cyrillic ............. . . 791 Preface Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg II. Non-classical Logics W. Rautenberg III. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. ProofTheory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. Each volume is divided into four main parts: 1) The Subject Index is arranged in sections by topics, usually corresponding to sections in the classification scheme; each section is ordered chronologically by year, and within a given year the items are listed alphabetically by author with the titles of the publications and their full classifications added. 2) The Author Index is ordered alphabetically by author, and contains the full bibliographical data of each publication together with its review numbers in Mathematical Reviews (MR), Zentralblatt flir Mathematik und ihre Grenzgebiete (Zbl), Journal of Symbolic Logic (JSL), and Jahrbuch iiber die Fortschritte der Mathematik (FdM). We much regret that we were not able to include reviews from Referativnyj Zhurnal Matematika in this edition. 3) The Source Index gives the full bibliographical data of each source (journals and books) for which only abbreviated forms are used in the Author Index. 4) The Miscellaneous Indexes contain various further indexes and tables to aid the reader in using the Bibliography. For a more detailed technical description of the Bibliography see the Table of Contents and the User's Guide. The uniform classification of all entries is a central feature of the Bibliography. The basic framework is the 03 section of the (1985 version of the) 1980 classifica tion scheme of Mathematical Reviews and Zentralblatt flir Mathematik und ihre Grenzgebiete. However, this has been modified in a number of ways. Indeed, the 1980 scheme was designed for the classification of works written after 1980, where as the majority of entries in the Bibliography come before this date. In some areas X Preface this has made the classification of older works difficult, and we have tried to cope with this by adding a few new sections and altering slightly the interpretation of others. We have not designated the classifications assigned to a work as primary and secondary, because of the difficulty in doing so in many cases. Each volume contains the full annotated classification scheme together with a description of its general features. In their introductions the Editors discuss specifically their inter pretations of the classification sections falling in their respective volumes. The Subject Index is another central feature of the Bibliography. Reading through this Index gives a historical perspective for each classification section and provides a rather quick overview of the literature in it. By browsing through the en tries of a specific area the reader may be rewarded by finding things (literature, subjects, questions) he was not aware of or had forgotten. An obvious question now is the extent to which one can rely on the complete ness and correctness of the Bibliography and on the accuracy of the classifications. We comment on each of these aspects separately. In an effort to be as complete as possible, we consulted all sources available to us and decided in favour of inclusion in doubtful cases (so that certainly some pa pers with little bearing on mathematical logic are listed here and there). As the his torical starting point for the Bibliography we chose the appearance of Frege's Be griffsschrift (1879). A certain restriction on scope stems from our decision to concentrate on mathematical logic and in particular on those areas defined by the titles of the six volumes. A major source of material was provided by the review journals mentioned above; we used them both to identify publications in the less known journals and to find review numbers and other bibliographical data of items found in other sources. We also made use of various lists of literature con tained in books, survey articles, mimeographed notes, etc. Some especially valu able newer sources were: W.Hodges: A Thousand Papers in Model Theory and Algebra M.A. McRobbie, A. Barcan and P. B. Thistlewaite: Interpolation Theorems: A Bi bliography D. S. Scott and J. M. B. Moss t: A Bibliography of Books on Symbolic Logic, Foun dations of Mathematics and Related Subjects C. A. B. Peacocke and D. S. Scott: A Selective Bibliography of Philosophical Logic. Various strategies and crosschecks were used to ensure the completeness of the bibliographical data and in particular of the reviews mentioned above. For each item listed in the Bibliography we tried to include any translations, reprintings in alternative sources and errata, and to give cross references for a work appearing in several parts. On the whole this Bibliography was compiled and organized for use by the practising mathematician; there is no claim that the most rigorous standards of li brarianship are met. It is hard to say how successful our striving for completeness was. This is espe cially true for the most recent literature. No 1986 items were included. We checked all the main journals in logic, the reviews in MR, Zbl and JSL and Current Mathe matical Publications for literature published up to the end of 1985, but undoubted ly some gaps remain. As for correctness, in any ordinary book we can tolerate a number of printing errors because of our knowledge of the language and the context, but, when one organizes data connected by (abstract) pointers in a computer program, almost every typing error has far-reaching consequences. Various consistency tests were used to check the program and the input data. There are, however, many other sources for mistakes and errors. For some items our references contained incomplete or ambiguous informa tion. Although we tried to complete the bibliographical data, this was often diffi cult, particularly in cases where, for example, the source was obscure or the pub- Preface XI lisher was given only by location. Another source of errors lies in the identification of author names. An author may publish using abbreviations of his first, his sec ond or both of his given names. This is generally not a problem for authors with uncommon surnames, but if the surname is, e.g., Smith or Brown the possibility of misidentification arises. We may have identified two different authors or failed to identify two or more different forms of an author name. It is unavoidable in a project of this scope that there will be errors, particularly in the classification, so perhaps it is worthwhile to explain briefly the process by which the classification was done. Items entered before 1981 were originally classi fied according to a scheme unrelated to the current one. To begin the conversion to the 1980 scheme we used the computer to change old categories to their new ver sions wherever there was a well-defined correspondence. Then every entry was checked and if necessary reclassified by hand. From 1981 each new entry was clas sified shortly after being entered in the database. For the most part this was done on the basis of titles, reviews, and other information, but without consulting the works themselves. This was necessary to preserve the finiteness of the enterprise, but it has inevitably led to errors, certainly in some cases egregious ones. These were constantly being corrected during the final editing process, but many will re main. Although the Editors have to some extent used different strategies in classify ing the entries falling into their respective volumes, finally a reasonable degree of uniformity has arisen. The user is referred to the Editors' introductions for further details on the classifying procedure. A special apology goes to the native speakers of languages with diacritical marks. Our central difficulty was to get the right spelling of names used in differ ent forms in such a variety of sources. In addition, entering diacritical marks in a computer introduces yet another source of errors; so they have almost all been ig nored (the User's Guide and the Miscellaneous Indexes contain details of those that have been transliterated). We appreciate that, although the absence of, for ex ample, accents in the text of a French title may not create undue problems, the lack of diacritical marks in author names is particularly unfortunate. We hope that this omission will not be too misleading. The future By its nature a bibliography has lasting value to the extent it succeeds in "complet ing the past". But it should also serve for some years as an aid to current research. We have various plans to extend the scope of the present Bibliography by includ ing new areas such as universal algebra, sheaves, philosophical logic (subdividing the present volumes I and II appropriately), and philosophy of mathematics. The present six volumes cover only approximately 80% of the data on our computer files. The possibility of extending the classification scheme by developing a so called thesaurus system was discussed on several occasions. Certainly this would be desirable; to some extent Alonzo Church tried to create such a system in connec tion with his bibliography in the Journal of Symbolic Logic. However there are dif ficult scientific problems connected with the creation of such a system and their solution requires much time and expertise. Another way to extend the Bibliography which would perhaps better serve the purpose of providing an overview of certain special areas would be to commission a series of survey papers to appear from time to time as, say, an additional issue of the Journal of Symbolic Logic; each paper would include an annotated listing of the literature taken from the Bibliography. There are plans to establish a bibliographical centre for Mathematical Logic and adjacent areas. A central function of such a centre would be to collect infor-