Set Theory and Hierarchy Theory A Memorial Tribute to Andrzej Mostowski PDF
Preview Set Theory and Hierarchy Theory A Memorial Tribute to Andrzej Mostowski
Lecture Notes ni Mathematics Edited by .A Dold and .B Eckmann 537 Set Theory and Hierarchy Theory A Memorial Tribute to Andrzej Mostowski Bierutowice, Poland 1975 Edited yb .W Marek, .M Srebrny dna .A Zarach galreV-regnirpS Berlin. Heidelberg (cid:12)9 NewYork 1976 Editors Wiktor Marek Institute of Mathematics University of Warsaw PKiN IX .p 00-901 Warszawa/Poland Marian Srebrny Mathematical Institute Polish Academy of Sciences P.O. Box 13 7 00-950 Warszawa/Poland Andrzej Zarach Institute of Mathematics Technical University ul. Wybrze~_e Wyspiar~skiego 27 50-370 WrocJ'aw/Poland Library of Congress Cataloging in Publication Data Conference on Set Theory and Hierarckly Theory, 2d, Bierutowiee, Poland, 1975. Set theory and hierarchy theory, Biertttowice, Poland, 1975. (Lecture notes in mathematics ; 537) i. Set theory--Congresses. 2. Model theory-- Congmesses. .3 Reeursive functions--Congresses. &. Mostowski, Andrzej--Bibliography. .I Marek, Wiktor. II. Srebrny, Marian, 1947- III. Za- ,l/cam Andrzej, 1948- IV. Title. V. Series: Lecture notes in mathematics (Berlin) ; 537. QA3. L28 vol. 537 QA248 510'.8s 511'.32 76-26534 AMS Subject Classifications (1970): 02F27, 02F2~), 02F35, 02H05, 02H13, 02 H15, 02K05, 02K10, 02 K30. ISBN 3-540-07856-8 Springer-Verlag Berlin (cid:12)9 Heidelberg (cid:12)9 New York ISBN 0-387-07856-8 Springer-Verlag New York (cid:12)9 Heidelberg (cid:12)9 Berlin This kro~v is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, re- printing, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage ni data banks. Under w 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 yb agreement with the publisher. (cid:14)9 by Springer-Verlag Berlin (cid:12)9 Heidelberg 1976 Printed in Germany Printing and binding: 8eltz Offsetdruck, Hemsbach/Bergstr IN MEMORIAM PROFESSOR ANDRZEJ MOSTOWSKI ANDRZEJ MOSTOWSKI November I, 1913 - August 22, 1975 FOREWORD This volume constitutes the Proceedings of the Second Conference on Set Theory and Hierarchy Theory held at the mountain resort of Bierutowice in Poland, Septen~er 17-28, 1975. This conference was organized and sponsored by the Institute of Mathematics of Technical University of Wroclaw. The programrL~e committee comprised Andrzej Mostowski (Warsaw), Czeslaw Ryll-Nardzewski (Wroclaw), Wiktor Marek (Warsaw), Leszek Pacholski (Wroc~aw), Bogdan W@glorz (Wroc~aw) and the organizing committee comprised Marian Srebrny (Warsaw), Jan Waszkiewicz (Wroclaw), Agnieszka Wojciechowska (WrocZaw), Andrzej Zarach (WrocZaw) - chairman. The conference was attended by 71 registered participants, of these 41 were from Poland. In view of the sudden death of Professor Mostowski we decided to dedicate this volume to his memory and to include a brief curriculum vitae, full bibliography of his works and an unpublished paper by him. Professor Mostowski contributed this paper to the similar conference held in 1974. Unfortunately, it has not been published yet. We wish to thank Mrs. M.Mostowska for her kind permission to include it to these Proceedings. The contributed papers are closely connected with Professor Mostowski's main topics of interest. During the conference a special session devoted to the memory of Professor Mostowski was held. We believe that these Proceedings constitute the participants' best tribute to him. On behalf of the organizing committee of the conference we wish to thank the Technical University of Wroclaw and all the people who by their help contributed to the success of the conference and its good scientific and friendly atmosphere. Special thanks are due to A. Wojciechowska and J.Waszkiewicz for their help in organizing the conference.We gratefuly acknowledge the assistance of Professor lllV G.H. MHller in suggesting the present form of the volume and for all his assitance in various stages of its preparation. We acknowledge also kind assistance of those who read and refereed the contributed papers (A.H.Lachlan, G.Wilmers and our colleagues from Warsaw and WrocZaw). Finally, we owe special gratitude to Miss T.Bochynek who had enough patience to expertly type all the manuscripts. March, 1976 Wiktor Marek Marian Srebrny Andrzej Zarach CONTENTS Curriculum vitae of A. MOSTOWSKI ........... I Bibliography of MOSTOWSKI'S works .......... 3 Two remarks on the models of Morse' set theory by A. MOSTOWSKI ............. 13 Contributed papers : . . . . . . . . . . . . . . . . . 23 B. BALCAR and W. GUZICKI, A remark on power of singular cardinals ............ 25 J. BELL, Uncountable standard models of ZFC + V ~ L 29 L. BUEDVSKY, Changing cofinality of ~2 ....... 37 D. CENZER, Inductive definitions positive and monotone . . . . . . . . . . . . . . . . . 51 K. DEVLIN, An alternative to Martin's axiom .... 65 M. DUBIEL, Elementary extension of ~-models ..... 77 U. FELGNER, Das Problem yon Souslin ft~r geordnete Strukturen ................ 83 S. GOTTWALD, A cumulative system of fuzzy sets . . . 109 S. KRAJEWSKI, Non standard satisfaction classes . . . 121 A. KRAWCZYK and M. KRYNICKI, Ehrenfeucht games for generalized quautifiers ......... 145 A. LACHLAN, Dimension and totally transcendental theories of rank 2 ........... 153 F. LOWENTHAL, Measure and categoricity in ~-recursion 185 W. MAREK and M. SREBRNY, Urelements and extendability 203 L. PACHOLSKI, On limit reduced powers, saturatedness and universality .... 221 S. ROGUSKI, Extensions of models for ZFC to models for ZF + V = HOD with applications 241 A. SLC~ON, Decision problems for generalized quantifiers - a survey ......... 249 A. SOCHOR, The alternative set theory ....... 259 J. TRUSS, Some cases of KGnig's Lemma ....... 273 Z. VETULANI, Categoricity relative to ordinals for models of set-theory and the nonabsoluteness of L ......... 285 M. WEESE, The universality of boolean algebras with the H~rtig quantifier ......... 291 W. ZADRO~NY, Von Neumann's hierarchy and definable reals . . . . . . . . . . . . . . . . . 297 A. ZARACH, Generic extension of admissible sets 321 P. HAjEK, Some Remarks on 8bservational model-theoretic languages .................. 335 LIST OF REGISTERED PARTICIPANTS Bohuslav Balcar Praha John Bell London lan Bergstra Utrecht Konrad Bieli~ski Kielce Piotr Borowik Cz~ stochowa Lev Bukovs~ Koslce v. Wojciech ~Buszkowski Pozna~ Douglas Cenzer Gainesville Jaroslav Chudacek Iv Praha Jacek Cicho~ Wroc law John Crossley Clayton Ber~d Dahn Berlin Keith Devlin l:11oB ' Malgorzata Dubiel Warszawa Arleta Dylu~ Wroc law Anna Fedyszak Warszawa Ulrich Felgner Heidelberg Adam Figura Wroclaw Siegfried Gottwald Leipzig Edward Grzegorek Wroclaw Andrze~ Grzegorczyk Warszawa Wojciech Guzicki Warszawa Petr Had I ek Praha Tomas /V Havr~uek Praha Czeslawa Jakubowicz Wroclaw Leena-Marij a Jauko Helsinki Laurence Kirby Manchester iIx Henryk Kotlarski Kielce Stauislaw Krajewski Warszawa Adam Krawczyk Warszawa Michal Krynicki Warszawa Wieslaw Kulaga Wroclaw Alistair Lachlan Vanc ouv e r Anna Lema~ska Warszawa Anna Lin Warszawa Francis Louveaux Paris Francis Lov enthal Brussel Wiktor Marek Warszawa Mariano Martinez Warszawa Tom Mc Laughlin Lubbock Roman Murawski Pozna~ Leszek Pacholski Wroc law Cecylia Rauszer Warszawa Stanislaw Roguski Wroclaw Michal Ryszkiewicz Warszawa Czes!aw Ryll-Nardzewski Wroclaw Detlef Seese Berlin Felice Serano Warszawa Kostas Skandalis Wroclaw Alan Slomson Leeds Anton Sochor Praha Krzysztof Sokolowski Warszawa Marian Srebrny Warszawa Petr St~p~uek Praha Zbigniew Szczepaniak Wroc~aw Rastislav Telg~rsky Wroclaw Jerzy Tomasik Wroc~aw John Truss Oxford
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