Set Theory and Hierarchy Theory V
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619 Set Theory and Hierarchy Theory V Bierutowice, Poland 1976
Edited by
A. Lachlan, M. Srebrny, and A. Zarach
Springer-Verlag Berlin Heidelberg NewYork 1977
Editors Alistair Lachlan Department of Mathematics Simon Fraser University Burnaby 2, B.C. V5A 1S6/Canada Marian Srebrny Mathematical Institute Polish Academy of Sciences P.O. Box 137 00-950 Warszawa/Poland Andrzej Zarach Institute of Mathematics Technical University ul. Wybrzeze Wyspiar'iskiego 27 50-370 Wroclaw/Poland
AMS Subject Classifications (1970): 02B20, 02B25, 02F29, 02H20, 02J05, 02K05, 02K10, 10N15, 54J05 ISBN 3-540-08521-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08521-1 Springer-Verlag New York Heidelberg Berlin 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, reuse 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 the publisher, the amount of the fee to be determined by agreement with the publisher.
© by SpringerVerlag Berlin Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
FOREWORD This volume represents the proceedings of the Third Conference on Set Theory and Hierarchy Theory held at Bierutowice a mountain resort south-west of Poland, September 17-24, 1976. It was organized by the Mathematical Institute of the Wroclaw Technical University. There were 62 registered participants representing 8 countries. The programme committee was: Alistair Lachlan /Canada/, Wiktor Marek /Warsaw/ , Janusz Onyszkiewicz /Warsaw/ , Leszek Pacholski /Wroclaw/, Marian Srebrny /Warsaw/, Bogdan /Wroclaw/, Wierzejewski /Wroclaw/- secretary, Andrzej Zarach /Wroclaw/ - chairman. We would like to express our appreciation to all those whose help contributed to the success of the conference. We are also gratefUl to all those who assisted us in giving these proceedings their present form. In particular: Gert H.MUller, Wiktor Marek, John Truss, Peter Hinman, Petr Hajek and many colleagues from Warsow and Wroclaw who helped us considerably in the editorial task.
April 1977
Alistair Lachlan Marian Srebrny Andrze j Zarach
CONTRIBUTED PAPERS: Z.Adamowicz, Construc1:iible semi - la1:itices of degrees of cons1:iruc1:iibility. • • • • • • • • • • • • • • 1 B.Balcar and P.Voj1:ias, Refining systems on Boolean .45 A. Baudisch and M. Weese, The Lindenbaum algebras of the theories of well-orderings and Abelian groups with the quantifier • • • • • • • 59 K. Bielinski, Extendability of structures as an infinitary property. • • • • • • • • • • • • • •
• • • 75
M.Boffa, A reduction of the theory of types • • • • • • .95 L.BukovskY, Random foroing. • • • • • • • • • • • • • • .101 J.Chuda6ek, Topological problems in Alternative Set Theory •• 119 J.Cichon, On the Baire property of Boolean algebras • • • • • 135 K.CUda, T
