An Outline of Mathematical Logic : Fundamental Results and Notions Explained with All Details

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handbooks and various piecemeal contribu­ tions and also sometimes to largely conceived "mathematical fol­ klore" of unpublished results.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. Since horses were first domesticated thousands of years ago, these iconic animals have been a part of human history - they've plowed our fields, pulled our carts, fought in our wars and been our beloved companions. Journey through the history of human and horse interaction in this beautifully illustrated history from the steady hand of American illustrator Jarom Vogel! Front Matter....Pages I-X Introduction to the Problems of the Foundations of Mathematics....Pages 1-64 The Classical Logical Calculus....Pages 65-262 Models of Axiomatic Theories....Pages 263-395 Logical Hierarchy of Concepts....Pages 396-564 Back Matter....Pages 565-596 See how the horse evolved from its ancient relatives, learn about famous horses from history and discover interesting facts along the way in this elegantly illustrated book.