The mathematics of logic: a guide to completeness theorems and their applications
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, t...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xii, 204 pages) |
| ISBN: | 9780511619243 |
| DOI: | 10.1017/CBO9780511619243 |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a König's lemma -- Posets and maximal elements -- Formal systems -- Deductions in posets -- Boolean algebras -- Propositional logic -- Valuations -- Filters and ideals -- First-order logic -- Completeness and compactness -- Model theory -- Nonstandard analysis | |
| 520 | |a This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis | ||
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Datensatz im Suchindex
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| author | Kaye, Richard |
| author_facet | Kaye, Richard |
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| author_sort | Kaye, Richard |
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| building | Verbundindex |
| bvnumber | BV043942930 |
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| contents | König's lemma -- Posets and maximal elements -- Formal systems -- Deductions in posets -- Boolean algebras -- Propositional logic -- Valuations -- Filters and ideals -- First-order logic -- Completeness and compactness -- Model theory -- Nonstandard analysis |
| ctrlnum | (ZDB-20-CBO)CR9780511619243 (OCoLC)850595857 (DE-599)BVBBV043942930 |
| 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 Philosophie |
| doi_str_mv | 10.1017/CBO9780511619243 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:39:18Z |
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| isbn | 9780511619243 |
| language | English |
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| spelling | Kaye, Richard Verfasser aut The mathematics of logic a guide to completeness theorems and their applications Richard Kaye Cambridge Cambridge University Press 2007 1 online resource (xii, 204 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) König's lemma -- Posets and maximal elements -- Formal systems -- Deductions in posets -- Boolean algebras -- Propositional logic -- Valuations -- Filters and ideals -- First-order logic -- Completeness and compactness -- Model theory -- Nonstandard analysis This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-70877-7 Erscheint auch als Druckausgabe 978-0-521-88219-4 https://doi.org/10.1017/CBO9780511619243 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kaye, Richard The mathematics of logic a guide to completeness theorems and their applications König's lemma -- Posets and maximal elements -- Formal systems -- Deductions in posets -- Boolean algebras -- Propositional logic -- Valuations -- Filters and ideals -- First-order logic -- Completeness and compactness -- Model theory -- Nonstandard analysis Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | The mathematics of logic a guide to completeness theorems and their applications |
| title_auth | The mathematics of logic a guide to completeness theorems and their applications |
| title_exact_search | The mathematics of logic a guide to completeness theorems and their applications |
| title_full | The mathematics of logic a guide to completeness theorems and their applications Richard Kaye |
| title_fullStr | The mathematics of logic a guide to completeness theorems and their applications Richard Kaye |
| title_full_unstemmed | The mathematics of logic a guide to completeness theorems and their applications Richard Kaye |
| title_short | The mathematics of logic |
| title_sort | the mathematics of logic a guide to completeness theorems and their applications |
| title_sub | a guide to completeness theorems and their applications |
| topic | Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Mathematische Logik |
| url | https://doi.org/10.1017/CBO9780511619243 |
| work_keys_str_mv | AT kayerichard themathematicsoflogicaguidetocompletenesstheoremsandtheirapplications |