Set Theory and Hierarchy Theory A Memorial Tribute to Andrzej Mostowski: Bierutowice, Poland 1975

339 Pages·1976·5.49 MB·English

by  Wiktor Marek

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
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(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