Higher Set Theory: Proceedings, Oberwolfach, Germany, April 13–23, 1977 PDF
Preview Higher Set Theory: Proceedings, Oberwolfach, Germany, April 13–23, 1977
Lecture Notes ni Mathematics Edited by A. Dold and B. Eckmann 669 rehgiH teS yroehT Proceedings, Oberwolfach, Germany, April 13-23, 1977 detidE yb G. H. MiJIler an - °--,~tt galreV-regnirpS Berlin Heidelberg New kroY 1978 Editors Gert H. M011er Mathematisches Institut Im Neuenheimer Feld 294 6900 Heidelberg/Germany Dana S. Scott Mathematical Institute 24-29 St. Giles Oxford OXl 3LB/England AMS Subject Classifications (1970): 02K05, 02K15, 02K30, 02K35, 02F27 ISBN 3-540-08926-8 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-08926-8 Springer-Verlag NewYerk 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, -er printing, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, dna storage ni data banks. Under § 54 of the namreG Copyright waL where copies are made for other than private ,esu a fee is payable to the publisher, the amount of the fee to eb determined by agreement with the publisher. © yb Springer-Verlag Berlin Heidelberg 8791 Printed ni Germany Printing dna binding: Beltz Offsetdruck, Hemsbach/Bergstr. 012345-0413/1412 : ~/i ~ ~ i ¸ ~ ~ii ~iii-~ ~i ¸ ~ ..... T: ~ i ~~ :i:~:~:~~ :i~ !~I~::~ :i~: :i ~ ~ /.~!!i i~ li~i i~ ~- ~TI---:~i:~ --~ MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH PREFACE A conference - originally intended to be on "Definability in Set Theory" - was held at the Mathematisches Forschungsinstitut Oberwolfach from the 13th to the 23rd of April 1977. As so often, the area covered by the speakers was larger than foreseen, so the title was changed by the Editors to the present one. It was a very intensive conference including three evening sessions, and many vivid and inspired dis- cussions took place. The conference was made possible by substantial help from the Heidelberger Akademie der Wissenschaften, which invited many of the participants to the meeting of the ~-group, and by the farseeing and generous support of the Oberwolfach Institute, which reserved an additional week for it and took over the participants of the a-meeting as guests in addition to further invitees. As always at Oberwolfach a welcome feeling of escape from the distractions of daily burdens grew out of the patient hospitality and unobtrusive but effective organization at the Institute. Knowing a little bit about the constant planning and work behind the creation and operation of such ~ refuge, we dedicate this volume as a small token of appreciation to the MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH and express our warmest thanks to its Director, Professor Martin BARNER and to Herrn Hans FOERSTENDORF and his kind and helpful crew. Gert H. MUller, Dana S. Scott ELBAT FO STNETNOC U.Felgner, T.B.Flannagan Wellordered subclasses of proper classes .......................... I H. Friedman A proof of foundation from axioms of cumulation .................. 15 Categoricity with respect to ordinals ............................ 17 Classically and intuitionistically provably recursive functions ... 21 K.Gloede Hierarchies of sets definable by means of infinitary languages .... 29 P.H~jek Some results on degrees of constructibility ....................... °55 H.R. Jervell Constructive universes I .......................................... 73 A.Kanamori, M~Magidor The evolution of large cardinal axioms in set theory .............. 99 A.S.Kechris Forcing in analysis .............................................. 277 A.Louveau Recursiveness and compactness ................................... 303 W.Maass Fine structure theory of the constructible universe in ~-and ~recursion theory ............................................. 339 W.Marek, P.Zbierski On a class of models of the n th order arithmetic .................. 361 A.R.D.Mathias O~and the p-point problem ....................................... 375 K.Mc Aloon A combinatorial characterization of inaccessible cardinals ....... 385 M.Srebrny Singular cardinals and analytic games .......................... 391 K.Steffens Regressive functions and stationary sets ....................... 423 P.{t~p~nek Cardinals in the inner model HOD ............................... 437 J.Stern Partitions of the real line into ~ ~I closed sets ............... 455 G.Takeuti G~del numbers of product spaces ................................ 461 J.Truss A note on increasing sequences of constructibility degrees ..... 473 ADDITIONAL TALKS GIVEN AT THE CONFERENCE Barwise, J. Global inductive definability 1 Drake, F. Higher type measurables from A2-determinacy Felgner, U. Constructibility and forcing in Ackermann's set theory Friedman, H. On the future development of set theory 1 Friedman, H. Hz - theorems needing ~l-rank Guzicki, W. On 2 nd order arithmetic with 2 ~ < -- n H~jek, P. Vopenka's alternative set theory 1 Harrington, L. Consistency of prewellordering of H3-sets of reals and an admissible set which should not be admitted Kanamori, A. Strong axioms of infinity Kechris, A. Souslin representations of projective sets and higher level analogs of L Louveau, A. Star games 1 Magidor, M. SatUrated ideals and Z~-sets Mc Aloon, K. Cuts and cardinals d'apr~s Kirby and Paris Prikry, K. Some remarks on measurability of reals Scott, D. Some problems in intuitionistic set theory Simpson, S. Choice schemata in 2nd-order arithmetic
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