The Fourteenth Annual Summer Research Institute, sponsored by the American
Mathematical Society and the Association for Symbolic Logic, was devoted to
Axiomatic Set Theory. Financial support was provided by a grant from the
National Science Foundation. The institute was held at the University of Cali-
fornia, Los Angeles, from July 10 to August 5, 1967, and was attended by more
than 125 participants. The Organizing Committee consisted of Paul J. Cohen,
Abraham Robinson (chairman), and Dana S. Scott (editor). Special thanks are
due to the Department of Mathematics of UCLA for providing facilities and
assistance which contributed in large measure to the excellent success of the
The program for the four weeks of the institute was organized into two ten-
lecture series, given by Dana S. Scott and Joseph R. Shoenfield, plus individual
contributions generally in one-hour sessions at the rate of four lectures per day.
By the last week this was reduced to three per day, as the strength of the partici-
pants had noticeably weakened. Nevertheless, most of the success of the institute
was due to the fact that nearly everyone attended all of the sessions.
The papers in this volume of the proceedings represent revised and generally
more detailed versions of the lectures presented at the institute. In view of the
large number of papers, which resulted in delaying the receipt of papers from some
authors, it was felt advisable to divide the proceedings into two volumes so as not
to delay the publication of these papers any longer.
DANA S. SCOTT