Recent years have seen the appearance of many English-Ianguage hand-
books of logie and numerous monographs on topieal discoveries in the
foundations of mathematies. These publications on the foundations of
mathematies as a whole are rather difficult for the beginners or refer
the reader to other handbooks and various pieeemeal eontribu- tions and
also sometimes to largely conceived "mathematical fol- klore" of
unpublished results. As distinct from these, the present book is as easy
as possible systematic exposition of the now classical results in the
foundations of mathematics. Henee the book may be useful especially for
those readers who want to have all the proofs carried out in full and
all the concepts explained in detail. In this sense the book is
self-contained. The reader's ability to guess is not assumed, and the
author's ambition was to reduce the use of sueh words as evident and
obvious in proofs to aminimum. This is why the book, it is believed, may
be helpful in teaehing or learning the foundation of mathematics in
those situations in which the student cannot refer to a parallel lecture
on the subject. This is also the reason that I do not insert in the book
the last results and the most modem and fashionable approaches to the
subjeet, which does not enrich the essential knowledge in founda- tions
but ean discourage the beginner by their abstract form. A. G.