A Course in Mathematical Logic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1977
|
| Schriftenreihe: | Graduate Texts in Mathematics
53 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothesis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathematics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presentation here is fairly standard, except that semantics occupies a very dominant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax |
| Beschreibung: | 1 Online-Ressource (XIII, 288 p) |
| ISBN: | 9781475743852 9781475743876 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-4385-2 |
Internformat
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| 500 | |a 1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothesis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathematics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presentation here is fairly standard, except that semantics occupies a very dominant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Manin, Jurij I. 1937-2023 |
| author_GND | (DE-588)121177580 |
| author_facet | Manin, Jurij I. 1937-2023 |
| author_role | aut |
| author_sort | Manin, Jurij I. 1937-2023 |
| author_variant | j i m ji jim |
| building | Verbundindex |
| bvnumber | BV042421615 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864106859 (DE-599)BVBBV042421615 |
| 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 | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4385-2 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781475743852 9781475743876 |
| issn | 0072-5285 |
| language | English |
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| series | Graduate Texts in Mathematics |
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| spelling | Manin, Jurij I. 1937-2023 Verfasser (DE-588)121177580 aut A Course in Mathematical Logic by Yu. I. Manin New York, NY Springer New York 1977 1 Online-Ressource (XIII, 288 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 53 0072-5285 1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothesis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathematics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presentation here is fairly standard, except that semantics occupies a very dominant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mathematische Logik (DE-588)4037951-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s 2\p DE-604 Graduate Texts in Mathematics 53 (DE-604)BV035421258 53 https://doi.org/10.1007/978-1-4757-4385-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Manin, Jurij I. 1937-2023 A Course in Mathematical Logic Graduate Texts in Mathematics Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4151278-9 |
| title | A Course in Mathematical Logic |
| title_auth | A Course in Mathematical Logic |
| title_exact_search | A Course in Mathematical Logic |
| title_full | A Course in Mathematical Logic by Yu. I. Manin |
| title_fullStr | A Course in Mathematical Logic by Yu. I. Manin |
| title_full_unstemmed | A Course in Mathematical Logic by Yu. I. Manin |
| title_short | A Course in Mathematical Logic |
| title_sort | a course in mathematical logic |
| topic | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mathematische Logik Einführung |
| url | https://doi.org/10.1007/978-1-4757-4385-2 |
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