In 1978 a Summer School in set theory of three weeks' duration was held in Cambridge, England, and was attended by about one hundred people. It was a most stimulating meeting, and the Organising Committee, Professor L. Harrington, Professor M. Magidor and the undersigned, here record their gratitude to the Scientific Affairs Division of NATO, who funded the meeting as an Advanced Study Institute; the Master and Fellows of Peterhouse; the Master and Fellows of Pembroke College; the University of Cambridge; and in particular to Mr and Mrs. J. F. Jenkins who ensured the smooth running of the whole. The names of participants with their addresses in 1978 are recorded at the end of the volume.

In some cases lecturers considered that adequate accounts of their topics were already in print or in press. This volume comprises five expository papers: those by Baumgartner, Guaspari and Stanley are developments of lectures presented at the meeting, those by Devlin and Kanamori, which expound topics complementing those of Baumgartner and Stanley respectively, were written independently of the meeting; and two research papers: those by Prikry and Shelah.