Ershov, Palyutin Mathematical Logic

Mathematical Logic
by Yu. L. Ershov, E. A. Palyutin.

This book presents in a systematic way a number of topics in modern
mathematical logic and the theory of algorithms. It can be used as
both a text book on mathematical logic for university students and
a text for specialist courses. The sections corresponding to the
obligatory syllabus (Sections 1 to 9 of Chapter 1,without the small
type, Sections 10 and 11 of Chapter 2, Sections 15 and 16 of Chapter
3,Sections 18 to 20, 22 and 23 of Chapter 4 and Section 35of Chapter
7) are written more thoroughly and in more detail than the sections
relating to more special questions.
The exposition of the propositional calculus and the calculus of
predicates is not a conventional one, beginning as it does with a
study of sequential variants of the calculi of natural deduction
( although the traditional calculi, referred to as Hilbertian,
also appears here). The reasons for this are:
A) the possibility of providing a good explanation of the meaning
of all the rules of inference;
B) the possibility of acquiring more rapidly the knack of making
formal proofs;
C) a practical opportunity of making all the formal proofs
necessary in the course for these calculi.

This book was translated from the Russian by Vladimir Shokurov. The
book was published by first Mir Publishers in 1984.

All credits to the original uploader.

DJVU | OCR | 4.3 MB | Pages: 302 |

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Table of Contents

Preface 7
INTRODUCTION 9

Chapter 1.
THE PROPOSITIONAL CALCULUS 15

Chapter 2.
SET THEORY 65

Chapter 3.
TRUTH ON ALGEBRAIC SYSTEMS 96

Chapter 4.
THE CALCULUS OF PREDICATES 117

Chapter 5.
MODEL THEORY 149

Chapter6.
PROOF THEORY 198

Chapter7.
ALGORITHMS AND RECURSIVE FUNCTIONS236

List of symbols 292
Subject Index 295