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Mathematical Logic /
This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no o...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York,
1994.
|
| Edición: | Second edition. |
| Colección: | Undergraduate texts in mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Ebbinghaus, H.-D. | |
| 245 | 1 | 0 | |a Mathematical Logic / |c by H.-D. Ebbinghaus, J. Flum, W. Thomas. |
| 250 | |a Second edition. | ||
| 260 | |a New York, NY : |b Springer New York, |c 1994. | ||
| 300 | |a 1 online resource (x, 290 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file | ||
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| 490 | 1 | |a Undergraduate Texts in Mathematics, |x 0172-6056 | |
| 520 | |a This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. | ||
| 505 | 0 | |a A -- I Introduction -- II Syntax of First-Order Languages -- III Semantics of First-Order Languages -- IV A Sequent Calculus -- V The Completeness Theorem -- VI The Löwenheim-Skolem and the Compactness Theorem -- VII The Scope of First-Order Logic -- VIII Syntactic Interpretations and Normal Forms -- B -- IX Extensions of First-Order Logic -- X Limitations of the Formal Method -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindström's Theorems -- References -- Symbol Index. | |
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mathematics. | |
| 650 | 0 | |a Logic, Symbolic and mathematical. | |
| 650 | 6 | |a Mathématiques. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 7 | |a applied mathematics. |2 aat | |
| 650 | 7 | |a mathematics. |2 aat | |
| 650 | 7 | |a Matemáticas |2 embne | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Mathematics |2 fast | |
| 700 | 1 | |a Flum, J. | |
| 700 | 1 | |a Thomas, W. | |
| 758 | |i has work: |a Mathematical logic (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGWvFYppbywchPvfRbWmtX |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |z 9781475723571 |
| 830 | 0 | |a Undergraduate texts in mathematics. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3084680 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH29489874 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL3084680 | ||
| 994 | |a 92 |b IZTAP | ||