Logic for mathematicians:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Chelsea Publ.
1978
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 563 - 568 |
| Physical Description: | XV, 574 S. graph. Darst. |
| ISBN: | 0828402949 |
Staff View
MARC
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| 245 | 1 | 0 | |a Logic for mathematicians |c J. Barkley Rosser |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Chelsea Publ. |c 1978 | |
| 300 | |a XV, 574 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz.: S. 563 - 568 | ||
| 650 | 4 | |a Logique symbolique et mathématique | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804116492071993344 |
|---|---|
| adam_text | CONTENTS
Preface vii
List of Symbols xii
chapter I. What Is Symbolic Logicf 1
1. A hypothetical interview 1
2. The role of symbolic logic 3
3. General nature of symbolic logic 5
4. Advantages and disadvantages of a symbolic logic ... 9
chapter II. The Statement Calculus 12
1. Statement functions 12
2. The dot notation 19
3. The use of truth value tables 23
4. Applications to mathematical reasoning 30
5. Summary of logical principles 46
chapter III. The Use of Names 49
chapter IV. Axiomatic Treatment of the Statement Calculus ... 54
1. The axiomatic method of denning valid statements ... 54
2. The truth value axioms 55
3. Properties of | 59
4. Preliminary theorems 60
5. The truth value theorem 68
6. The deduction theorem 75
chapter V. Clarification 77
chapter VI. The Restricted Predicate Calculus 82
1. Variables and unknowns 82
2. Quantifiers 87
3. Axioms for the restricted predicate calculus 101
4. The generalization principle 103
5. The equivalence and substitution theorems 107
6. Useful equivalences 112
iz
x CONTENTS
7. The formal analogue of an act of choice 123
8. Restricted quantification 140
9. Applications to everyday mathematics 150
10. Church s theorem I61
11. A convention concerning bound variables 162
chapter VII. Equality 163
1. General properties 163
2. Enumerative quantifiers 166
3. Applications 172
chapter VIII. Descriptions 181
1. Axioms for descriptions 181
2. Definition by cases 187
3. Uses of descriptions in everyday mathematics .... 195
chapter IX. Class Membership 197
1. The notion of a class 197
2. Axioms for classes 207
3. Formalism for classes 219
4. The calculus of classes 226
5. Manifold products and sums 238
6. Unit classes and subclasses 249
7. Variables over the range 2 256
8. Applications 263
chapter X. Relations and Functions 275
1. The axiom of infinity 275
2. Ordered pairs and triples 280
3. The calculus of relations 284
4. Special properties of relations 294
5. Functions 305
6. Ordered sets 330
7. Equivalence relations 339
8. Applications 344
chapter XI. Cardinal Numbers 345
1. Cardinal similarity 345
2. Elementary properties of cardinal numbers 371
3. Finite classes and mathematical induction 390
4. Denumerable classes 429
5. The cardinal number of the continuum 444
6. Applications 451
CONTENTS xi
chapter XII. Ordinal Numbers 456
1. Ordinal similarity 456
2. Well ordering relations 459
3. Elementary properties of ordinal numbers 470
4. The cardinal number associated with an ordinal number . 477
5. Applications 481
chapter XIII. Counting 483
1. Preliminaries 483
2. The axiom of counting 485
3. The pigeonhole principle 487
4. Applications 488
chapter XIV. The Axiom of Choice 490
1. The general axiom of choice 490
2. How indispensable is the axiom of choice? 510
3. The denumerable axiom of choice 512
chapter XV. We Rest Our Case 517
appendix A. A Proof of the Axiom of Infinity 525
appendix B. The Axiom of Counting 538
appendix C. The Axiom of Choice 540
appendix D. Nonstandard Analysis 542
Bibliography 563
Index 571
|
| any_adam_object | 1 |
| author | Rosser, John Barkley 1907-1989 |
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| author_facet | Rosser, John Barkley 1907-1989 |
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| author_sort | Rosser, John Barkley 1907-1989 |
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| callnumber-first | B - Philosophy, Psychology, Religion |
| callnumber-label | BC135 |
| callnumber-raw | BC135 |
| callnumber-search | BC135 |
| callnumber-sort | BC 3135 |
| callnumber-subject | BC - Logic |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)2963692 (DE-599)BVBBV002041705 |
| dewey-full | 511/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.3 |
| dewey-search | 511/.3 |
| dewey-sort | 3511 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002041705 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:39:22Z |
| institution | BVB |
| isbn | 0828402949 |
| language | English |
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| oclc_num | 2963692 |
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| physical | XV, 574 S. graph. Darst. |
| psigel | TUB-www |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Chelsea Publ. |
| record_format | marc |
| spelling | Rosser, John Barkley 1907-1989 Verfasser (DE-588)129075728 aut Logic for mathematicians J. Barkley Rosser 2. ed. New York Chelsea Publ. 1978 XV, 574 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz.: S. 563 - 568 Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001335207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosser, John Barkley 1907-1989 Logic for mathematicians Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Logic for mathematicians |
| title_auth | Logic for mathematicians |
| title_exact_search | Logic for mathematicians |
| title_full | Logic for mathematicians J. Barkley Rosser |
| title_fullStr | Logic for mathematicians J. Barkley Rosser |
| title_full_unstemmed | Logic for mathematicians J. Barkley Rosser |
| title_short | Logic for mathematicians |
| title_sort | logic for mathematicians |
| topic | Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematische Logik |
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