Recent years have seen the appearance of many English-language hand
books of logic and numerous monographs on topical discoveries in
the foundations of mathematics. These publications on the
foundations of mathematics as a whole are rather difficult for the
beginners or refer the reader to other handbooks and various
piecemeal contribu 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"mathematical fol klore" of unpublished results.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. Hence 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 such words as
evident and obvious in proofs to a minimum. This is why the book,
it is believed, may be helpful in teaching 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 subject, which does
not enrich the essential knowledge in founda tions but can
discourage the beginner by their abstract form. A. G."
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