Classical mathematical logic: the semantic foundations of logic
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton
Princeton University Press
©2006
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and indexes Classical propositional logic -- Abstracting and axiomatizing classical propositional logic -- The language of predicate logic -- The semantics of classical predicate logic -- Substitutions and equivalences -- Equality -- Examples of formalization -- Functions -- The abstraction of models -- Axiomatizing classical predicate logic -- The number of objects in the universe of a model -- Formalizing group theory -- Linear orderings -- Second-order classical predicate logic -- The natural numbers -- The integers and rationals -- The real numbers -- One-dimensional geometry -- Two-dimensional Euclidean geometry -- Translations within classical predicate logic -- Classical predicate logic with non-referring names -- The Liar paradox -- On mathematical logic and mathematics -- Appendix: The completeness of classical predicate logic proved by Gödel's Method In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proo |
| Beschreibung: | 1 Online-Ressource (xxii, 522 pages) |
| ISBN: | 0691123004 1400841550 9780691123004 9781400841554 |
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| 500 | |a Includes bibliographical references and indexes | ||
| 500 | |a Classical propositional logic -- Abstracting and axiomatizing classical propositional logic -- The language of predicate logic -- The semantics of classical predicate logic -- Substitutions and equivalences -- Equality -- Examples of formalization -- Functions -- The abstraction of models -- Axiomatizing classical predicate logic -- The number of objects in the universe of a model -- Formalizing group theory -- Linear orderings -- Second-order classical predicate logic -- The natural numbers -- The integers and rationals -- The real numbers -- One-dimensional geometry -- Two-dimensional Euclidean geometry -- Translations within classical predicate logic -- Classical predicate logic with non-referring names -- The Liar paradox -- On mathematical logic and mathematics -- Appendix: The completeness of classical predicate logic proved by Gödel's Method | ||
| 500 | |a In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proo | ||
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| 650 | 7 | |a MATHEMATICS / Infinity |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Logic |2 bisacsh | |
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| 650 | 7 | |a Semantics (Philosophy) |2 fast | |
| 650 | 7 | |a Wiskundige logica |2 gtt | |
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| 650 | 7 | |a Mathematische Logik |2 swd | |
| 650 | 7 | |a Philosophische Semantik |2 swd | |
| 650 | 4 | |a Semantik | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Semantics (Philosophy) | |
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Datensatz im Suchindex
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| author | Epstein, Richard L. |
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| 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 |
| format | Electronic eBook |
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| isbn | 0691123004 1400841550 9780691123004 9781400841554 |
| language | English |
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| spelling | Epstein, Richard L. Verfasser aut Classical mathematical logic the semantic foundations of logic Richard L. Epstein ; with contributions by Lesław W. Szczerba Princeton Princeton University Press ©2006 1 Online-Ressource (xxii, 522 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and indexes Classical propositional logic -- Abstracting and axiomatizing classical propositional logic -- The language of predicate logic -- The semantics of classical predicate logic -- Substitutions and equivalences -- Equality -- Examples of formalization -- Functions -- The abstraction of models -- Axiomatizing classical predicate logic -- The number of objects in the universe of a model -- Formalizing group theory -- Linear orderings -- Second-order classical predicate logic -- The natural numbers -- The integers and rationals -- The real numbers -- One-dimensional geometry -- Two-dimensional Euclidean geometry -- Translations within classical predicate logic -- Classical predicate logic with non-referring names -- The Liar paradox -- On mathematical logic and mathematics -- Appendix: The completeness of classical predicate logic proved by Gödel's Method In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proo Logique symbolique et mathématique Sémantique (Philosophie) MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Logic, Symbolic and mathematical fast Semantics (Philosophy) fast Wiskundige logica gtt Semantiek gtt Mathematische Logik swd Philosophische Semantik swd Semantik Logic, Symbolic and mathematical Semantics (Philosophy) http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=413296 Aggregator Volltext |
| spellingShingle | Epstein, Richard L. Classical mathematical logic the semantic foundations of logic Logique symbolique et mathématique Sémantique (Philosophie) MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Logic, Symbolic and mathematical fast Semantics (Philosophy) fast Wiskundige logica gtt Semantiek gtt Mathematische Logik swd Philosophische Semantik swd Semantik Logic, Symbolic and mathematical Semantics (Philosophy) |
| title | Classical mathematical logic the semantic foundations of logic |
| title_auth | Classical mathematical logic the semantic foundations of logic |
| title_exact_search | Classical mathematical logic the semantic foundations of logic |
| title_full | Classical mathematical logic the semantic foundations of logic Richard L. Epstein ; with contributions by Lesław W. Szczerba |
| title_fullStr | Classical mathematical logic the semantic foundations of logic Richard L. Epstein ; with contributions by Lesław W. Szczerba |
| title_full_unstemmed | Classical mathematical logic the semantic foundations of logic Richard L. Epstein ; with contributions by Lesław W. Szczerba |
| title_short | Classical mathematical logic |
| title_sort | classical mathematical logic the semantic foundations of logic |
| title_sub | the semantic foundations of logic |
| topic | Logique symbolique et mathématique Sémantique (Philosophie) MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Logic, Symbolic and mathematical fast Semantics (Philosophy) fast Wiskundige logica gtt Semantiek gtt Mathematische Logik swd Philosophische Semantik swd Semantik Logic, Symbolic and mathematical Semantics (Philosophy) |
| topic_facet | Logique symbolique et mathématique Sémantique (Philosophie) MATHEMATICS / Infinity MATHEMATICS / Logic Logic, Symbolic and mathematical Semantics (Philosophy) Wiskundige logica Semantiek Mathematische Logik Philosophische Semantik Semantik |
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