The aim of this monograph is to present some of the basic ideas and
results in pure combinatory logic and their applications to some
topics in proof theory, and also to present some work of my own.
Some of the material in chapter 1 and 3 has already appeared in my
notes Introduction to Combinatory Logic. It appears here in revised
form since the presen tation in my notes is inaccurate in several
respects. I would like to express my gratitude to Stig Kanger for
his invalu able advice and encouragement and also for his
assistance in a wide variety of matters concerned with my study in
Uppsala. I am also in debted to Per Martin-USf for many valuable
and instructive conversa tions. As will be seen in chapter 4 and 5,
I also owe much to the work of Dag Prawitz and W. W. Tait. My
thanks also to Craig McKay who read the manuscript and made
valuable suggestions. I want, however, to emphasize that the
shortcomings that no doubt can be found, are my sole
responsibility. Uppsala, February 1972."
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