Logic and Structure:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Ausgabe: | Third, Augmented Edition |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A book which efficiently presents the basics of propositional and predicate logic, van Dalen’s popular textbook contains a complete treatment of elementary classical logic, using Gentzen’s Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Löwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions. The discussion of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. Completeness is established for Kripke semantics. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property have been incorporated. The power and elegance of natural deduction is demonstrated best in the part of proof theory called 'cut-elimination' or 'normalization'. Chapter 6 is devoted to this topic; it contains the basic facts on the structure of derivations, both classically and intuitionistically. Finally, this edition contains a new chapter on Gödel's first incompleteness theorem. The chapter is self-contained, it provides a systematic exposition of primitive recursion and partial recursive functions, recursive by enumerable sets, and recursive separability. The arithmetization of Peano's arithmetic is based on the natural deduction system |
| Beschreibung: | 1 Online-Ressource (X, 220 p) |
| ISBN: | 9783662029626 9783540578390 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-662-02962-6 |
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| 500 | |a A book which efficiently presents the basics of propositional and predicate logic, van Dalen’s popular textbook contains a complete treatment of elementary classical logic, using Gentzen’s Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Löwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions. The discussion of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. Completeness is established for Kripke semantics. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property have been incorporated. The power and elegance of natural deduction is demonstrated best in the part of proof theory called 'cut-elimination' or 'normalization'. Chapter 6 is devoted to this topic; it contains the basic facts on the structure of derivations, both classically and intuitionistically. Finally, this edition contains a new chapter on Gödel's first incompleteness theorem. The chapter is self-contained, it provides a systematic exposition of primitive recursion and partial recursive functions, recursive by enumerable sets, and recursive separability. The arithmetization of Peano's arithmetic is based on the natural deduction system | ||
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Datensatz im Suchindex
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| author | Dalen, Dirk |
| author_facet | Dalen, Dirk |
| author_role | aut |
| author_sort | Dalen, Dirk |
| author_variant | d d dd |
| building | Verbundindex |
| bvnumber | BV042423229 |
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| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165449465 (DE-599)BVBBV042423229 |
| 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 | 10.1007/978-3-662-02962-6 |
| edition | Third, Augmented Edition |
| format | Electronic eBook |
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| spelling | Dalen, Dirk Verfasser aut Logic and Structure by Dirk Dalen Third, Augmented Edition Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (X, 220 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 A book which efficiently presents the basics of propositional and predicate logic, van Dalen’s popular textbook contains a complete treatment of elementary classical logic, using Gentzen’s Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Löwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions. The discussion of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. Completeness is established for Kripke semantics. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property have been incorporated. The power and elegance of natural deduction is demonstrated best in the part of proof theory called 'cut-elimination' or 'normalization'. Chapter 6 is devoted to this topic; it contains the basic facts on the structure of derivations, both classically and intuitionistically. Finally, this edition contains a new chapter on Gödel's first incompleteness theorem. The chapter is self-contained, it provides a systematic exposition of primitive recursion and partial recursive functions, recursive by enumerable sets, and recursive separability. The arithmetization of Peano's arithmetic is based on the natural deduction system 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 2\p (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Logik (DE-588)4037951-6 s 3\p DE-604 https://doi.org/10.1007/978-3-662-02962-6 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dalen, Dirk Logic and Structure 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 (DE-588)4123623-3 |
| title | Logic and Structure |
| title_auth | Logic and Structure |
| title_exact_search | Logic and Structure |
| title_full | Logic and Structure by Dirk Dalen |
| title_fullStr | Logic and Structure by Dirk Dalen |
| title_full_unstemmed | Logic and Structure by Dirk Dalen |
| title_short | Logic and Structure |
| title_sort | logic and structure |
| 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 Lehrbuch |
| url | https://doi.org/10.1007/978-3-662-02962-6 |
| work_keys_str_mv | AT dalendirk logicandstructure |