The 1990 European Summer Meeting of the Association for Symbolic Logic was held in Finland from July 15 to July 22, 1990. The meeting was called Logic Colloquium '90 and it took place in the Porthania building of the University of Helsinki as part of the program of the 350th anniversary of the university.

The meeting was attended by 140 registered participants and 31 accompanying persons, from 23 different countries. The organizing bodies were the Department of Mathematics of the University of Helsinki, The Philosophical Society of Finland, and The Finnish Mathematical Society. Financial support was received from the Ministry of Education of Finland, The Academy of Finland, Suomen Kulttuurirahasto Foundation, UNESCO, Rolf Nevanlinna Institute, and IUHPS.

The Organizing Committee of the meeting consisted of Aapo Halko, Heikki Heikkila, Lauri Hella, Taneli Huuskonen, Tapani Hyttinen, Kerkko Luosto, Ilkka Niiniluoto (vice chairman), Juha Oikkonen, and Jouko Vaananen (chairman), all from the University of Helsinki.

The Program Committee consisted of Peter Aczel (Manchester), Max Dickmann (Paris), Heinz-Dieter Ebbinghaus (Freiburg), Jens Fenstad (Oslo), Jaakko Hintikka (chairman, Boston), Wilfrid Hodges (London), Alistair Lachlan (Vancouver), Azriel Levy (Jerusalem), Heikki Mannila (Helsinki), Ilkka Niiniluoto (Helsinki), Juha Oikkonen (Helsinki), and Jouko Vaananen (secretary, Helsinki).

The program of the meeting is listed on the following pages. Warren Goldfarb, Ronald Jensen, Phokion Kolaitis, Per Martin-Lδf, Alan Mekler, and Hugh Woodin did not contribute a paper to the proceedings. As comparison between the contents of this book and the actual program reveals, some authors made an agreement with the editors to contribute a slightly different paper from the one read in the meeting. Also Joan Moschovakis and Alan Silver were approached by the editors and they submitted the paper they read in a contributed papers session of the meeting.

The editors are indebted to Heikki Heikkila, Yiannis Moschovakis, Martti Nikunen, and Hannele Salminen for their help during the preparation of this volume. We owe special thanks to Herbert Enderton for the substantial work he has done in putting together the final manuscript.