Journal Symbolic Logic

THE JOURNAL OF SYMBOLIC LOGIC

EDITED BY

WILLIAM CRAIG KIT FINE YIANNIS MOSCHOVAKIS

HERBERT ENDERTON,,' DAGFINN FQLLESDAL ANIL NERODE

WILFRID HODGES

Managing Editor: ALFONS BORGERS • /

Consulting Editors: y

PETER ACZEL DAVID KAPLAN GABRIEL SABBAGH JIRIBECYAR SAUL A. KRIPKE GERALD SACKS JOAN BRESNAN MICHAEL MAKKAI ARTO SALOMAA M. J. CRESSWJELL RUTH BARCAN MARCUS DANA S. SCOTT

MARTIN D. DAVIS DONALD A. MARTIN JOSEPH R. SHOENFIELD U SOLOMON FEFERMAN J. DONALD MONK - RICHARD A. SHORE FREDERIC B. FITCH GERTH.MULLER BAS VAN FRAASSEN CHARLES D. PARSPNS •

VOLUME 45 • NUMBER 2 • JUNE 1980

ISSN0G22-4«12

PUBLISHED QUARTERLY BY THE ASSOCIATION FOR SYMBOLIC'LOGIC, INC. WITH SUPPORT FROM ICSU AND FROM INSTITUTIONAL AND CORPORATE MEMBERS

Copyright C 1980 by the Association for Symbolic Logic, Inc. . Reproduction by photostat, photo-print, microfilm, or 'like process by permission only

Downloaded from https://www.cambridge.org/core. IP address: 170.106.35.234, on 02 Oct 2021 at 04:06:09, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0022481200046715 TABLE OF CONTENTS Substance and first-order quantification over individual-concepts. By JOHN BACON 193 Jumping through the transfinite: the master code hierarchy of Turing degree*. By-, HAROLD T. HODES ;.„.... ., ?. ,v....^ 204 The lattice of modal logics: an algebraic investigation. By W. J. BLOK...... i. 221 Constructive models of subsystems of ZF. By RICHARD GOSTANIAN ,^.....,..^. 237 A strengthening of Jensen's • principles. By AARON BELLER and AMI LITMAN...... 251 On the elementary equivalence of automorphism groups of Boolean algebras; down ward Skolem Lowenheim theorems and compactness of related quantifiers. By MATATYAHU RUBIN and SAHARON SHELAH ....j...., 265

On N0-categorical nilrings. II. By GREGORY CHERLIN ...... ,„.„...:.....>. 291 Theories with exactly three countable models and theories with algebraic prime

models. By ANAND PILLAY .^...r...... ^.. 302 The equational theory of GA3 is undecidable. By ROGER MADDUX 311 Recursion theory on orderings. II. By J. B. REMMEL : 317 On the bounded monadic theory of well-ordered structures. By WOLFGANG THOMAS 334 Sequential method in quantum logic. By HIROKAZU NISHIMURA j„ 339"- On computational complexity in weakly admissible structures. By VIGGO :

STOLTENBERG -HANSEN „ L^...,r.L... 353 Some theories associated with algebraically closed fields. By CHRIS ASH and JOHN ROSENTHAL ,. .X,.;.>.... \ 359 Innocuous substitutions. By DANIEL LEIVANT ...„ 363 Reviews .» „ * 369 European meeting of the Association for Symbolic Logic, Mons, Belgium, 1978. By M. BOFFA and P. HENRARD .» 386 Abstracts of papers \..~. 386

Notices : r.. 415

THE JOURNAL OF SYMBOLIC LOGIC is published quarterly, in the months of March, June, September, and December. The JOURNAL is the official organ of the Association for Symbolic Logic, Inc., an inter national organization for furthering research in symbolic logic and exchange of ideas among mathemati cians, philosophers, and others interested in this field. Individual membership in the Association is open to anyone interested in its work. Annual dues for stu dents are $9.00. Dues for other individual members are $18,00 per year. Dues include subscription to the ^ current volume of the JOURNAL. For their personal use, members may purchase back volumes at 25% dis count, i : - • •• t Institutional membership in the Association is available to any academic institution or department. An nual dues are $120.00. Membership privileges include choices of current subscriptions, of back volumes, and of student memberships; a detailed description is available from the Association. Information on cor porate membership is also available from the Association. ' Continued on inside back cover Second-class postage rates paid at Providence, RI, and additional offices