The present treatise belongs to the metamathematics of Algebra. The fact that this subject has in recent years attracted the active
attention of various eminent logicians has encouraged the present
author to contribute to it yet another monograph. A general
survey of the contents will be found in the first section of the first
chapter. Except where references to earlier papers are given, the
methods and results described here were obtained within the last
twelve months. Some of the work was reported upon in lectures
in Zurich (June, 1954) and Jerusalem (July, 1954) and at the
Symposium on the mathematical interpretation of formal systems,
which was held in conjunction with the International Congress of
Mathematicians (Amsterdam, September, 1954).