Journal Symbolic Logic

THE JOURNAL OF SYMBOLIC LOGIC

EDITED BY

WILLIAM CRAIG KIT FINE YLANNIS MOSCHOVAKIS

HERBERT ENDERTON DAGFINN F0LLESDAL ANIL NERODE

WILFRID HODGES

Managing Editor: ALFONS BORGERS

Consulting Editors:

PETER ACZEL FREDERIC B. FITCH GERT H MULLER JIRI' BECVAR HANS KAMP CHARLES D. PARSONS GEORGE BOOLOS DAVID KAPLAN GABRIEL SABBAGH JOAN BRESNAN SAUL A KRIPKE GERALD SACKS JOHN P. BURGESS KENNETH KUNEN ARTO SALOMAA STEPHEN A COOK MICHAEL MAKKAI DANA S. SCOTT M J. CRESSWELL RUTH BARCAN MARCUS JOSEPH R SHOENFIELD MARTIN D. DAVIS DONALD A. MARTIN RICHARD A. SHORE SOLOMON FF.FERMAN J. DONALD MONK STEVEN K THOMASON JENS ERIK FENSTAD BAS VAN FRAASSEN

VOLUME 46 • NUMBER 4 • DECEMBER 1981 ISSN 0022-4812

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

Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.226, on 26 Sep 2021 at 20:04:34, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0022481200044996 TABLE OF CONTENTS

The upper semilattice by degrees < 0' is complemented. By DAVID B. POSNKR .. 705 Degrees joining to 0'. By DAVID B. POSNER and ROBERT W. ROBINSON 714 Degrees of structures. By LINDA JEAN RICHTER 723 The model of set theory generated by countably many generic reals. By ANDREAS BLASS 732 Upper bounds on locally countable admissible initial segments of a Turing degree hierarchy. By HAROLD T. HODES 753 Undecidable L* theories of topological abelian groups. By GREGORY L. CHERLIN and PETER H. SCHMITT 761 Equivalence between semantics for intuitionism. I. By E. G. K. LOPEZ-ESCOBAR 773 Stability of nilpotent groups of class 2 and prime exponent. By ALAN H. MEKLER 781 Partial orderings of fixed finite dimension: Model companions and density. By ALFRED B. MANASTER and JEFFREY B. REMMEL 789 Forcing with A perfect trees and minimal A-degrees. By ALEXANDER S. KECHRIS 803 The equivalence of a generalized Martin's axiom to a combinatorial principle. By WILLIAM WEISS 817 AD and the supercompactness of ttj. By HOWARD BECKER 822 The model-theoretic significance of complemented existential formulas. By VOLKER WEISPFENNING 843 Effective aspects of profinite groups. By RICK L. SMITH 851 Reviews 864 List of officers and members of the Association for Symbolic Logic 881 Index of reviews 914 Notices 919

THK JOURNAL OI- 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. 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.

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