## Mathematical Logic – Ershov, Palyutin

In this post we will see 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 sectionsrelating 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 |

Preface 7
INTRODUCTION 9
Chapter 1.
THE PROPOSITIONAL CALCULUS 15
1. Sets and words 15
2. The language of the propositional calculus 21
3. Axiom system and rules of inference 25
4. The equivalence of formulas 32
5. Normal forms35
6. Semantics of the propositional calculus 43
7. Characterization of provable formula 48
8. Hilbertian propositional calculus 52
9. Conservative extension of calculi 56

Chapter 2.
SET THEORY 65

10. Predicates and mappings 65
11. Partially ordered sets 70
12. Filters of Boolean algebra 78
13.The power of a set 82
14.The axiom of choice 90

Chapter 3.
TRUTH ON ALGEBRAIC SYSTEMS 96

15. Algebraic systems96
16. Formulas of the signature \$\Sigma\$ 102
17. Compactness theorem110

Chapter 4.
THE CALCULUS OF PREDICATES 117
18. Axioms and rules of inference 117
19. The equivalence of formulas 126
20. Normal forms 130
21. Theorem on the existence of a model 132
22. Hilbertian calculus of predicates 139
23. Pure calculus of predicates 144

Chapter 5.
MODEL THEORY 149

24. Elementary equivalence 149
25. Axiomatizable classes 157
26. Skolem functions 165
27. Mechanism of compatibility 168
28. Countable homogeneity and universality 181
29. Categoricity 188

Chapter6.
PROOF THEORY 198

30. The Gentzen system G 198
31. The invertibility of rules 204
32. Comparison of the calculi \$CP^\Sigma\$ and G 210
33. Herbrand theorem 217
34. The calculi of resolvents 228

Chapter7.
ALGORITHMS AND RECURSIVE FUNCTIONS236

35. Normal algorithms and Turing machines 236
36. Recursive functions 247
37. Recursively enumerable predicates 264
38. Undecidability of the calculus of predicates and Godel’s incompleteness theorem 276
List of symbols 292
Subject Index  295

### 9 Responses to Mathematical Logic – Ershov, Palyutin

1. m95 says:

Thanks for this nice post

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2. m95 says:

very nice post, appreciated effort, thanks a lot

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3. VJ says:

This book link is not active.
could you please post this file.
Thanks,

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• desperadomar says:

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4. Ravishankar says:

the fle is corrupt and not opening

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• desperadomar says:

The file is in good condition.I just checked now.Hope you are facing issues in opening the file.Please read FAQs.

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5. https://ybaljawordpress.com says:

Reblogged this on ybalja and commented:
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 sectionsrelating 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 |
You can get the book here
For magnet / torrent links go here.

Password, if required, for 4shared files:

http://www.mirtitles.org

Facing problems while extracting? See FAQs

Preface 7
INTRODUCTION 9
Chapter 1.
THE PROPOSITIONAL CALCULUS 15
1. Sets and words 15
2. The language of the propositional calculus 21
3. Axiom system and rules of inference 25
4. The equivalence of formulas 32
5. Normal forms35
6. Semantics of the propositional calculus 43
7. Characterization of provable formula 48
8. Hilbertian propositional calculus 52
9. Conservative extension of calculi 56

Chapter 2.
SET THEORY 65

10. Predicates and mappings 65
11. Partially ordered sets 70
12. Filters of Boolean algebra 78
13.The power of a set 82
14.The axiom of choice 90

Chapter 3.
TRUTH ON ALGEBRAIC SYSTEMS 96

15. Algebraic systems96
16. Formulas of the signature \$\Sigma\$ 102
17. Compactness theorem110

Chapter 4.
THE CALCULUS OF PREDICATES 117
18. Axioms and rules of inference 117
19. The equivalence of formulas 126
20. Normal forms 130
21. Theorem on the existence of a model 132
22. Hilbertian calculus of predicates 139
23. Pure calculus of predicates 144

Chapter 5.
MODEL THEORY 149

24. Elementary equivalence 149
25. Axiomatizable classes 157
26. Skolem functions 165
27. Mechanism of compatibility 168
28. Countable homogeneity and universality 181
29. Categoricity 188

Chapter6.
PROOF THEORY 198

30. The Gentzen system G 198
31. The invertibility of rules 204
32. Comparison of the calculi \$CP^\Sigma\$ and G 210
33. Herbrand theorem 217
34. The calculi of resolvents 228

Chapter7.
ALGORITHMS AND RECURSIVE FUNCTIONS236

35. Normal algorithms and Turing machines 236
36. Recursive functions 247
37. Recursively enumerable predicates 264
38. Undecidability of the calculus of predicates and Godel’s incompleteness theorem 276
List of symbols 292
Subject Index 295

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6. https://ybaljawordpress.com says:

thank u v m

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