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Record Nr. |
UNINA9910786641503321 |
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Autore |
Hatcher William S. |
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Titolo |
The logical foundations of mathematics / / by William S. Hatcher |
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Pubbl/distr/stampa |
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Oxford, England : , : Pergamon Press, , 1982 |
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©1982 |
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ISBN |
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Edizione |
[First edition.] |
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Descrizione fisica |
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1 online resource (331 p.) |
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Collana |
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Foundations and Philosophy of Science and Technology Series |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front Cover; The Logical Foundations of Mathematics; Copyright Page; Dedication; Preface; Table of Contents; Chapter 1. First-order Logic; 1.1. The sentential calculus; 1.2. Formalization; 1.3. The statement calculus as a formal system; 1.4. First-order theories; 1.5. Models of first-order theories; 1.6. Rules of logic; natural deduction; 1.7. First-order theories with equality; variable-binding term operators; 1.8. Completeness with vbtos; 1.9. An example of a first-order theory; Chapter 2. The Origin of Modern Foundational Studies; 2.1. Mathematics as an independent science |
2.2. The arithmetization of analysis2.3. Constructivism; 2.4. Frege and the notion of a formal system; 2.5. Criteria for foundations; Chapter 3. Frege's System and the Paradoxes; 3,1. The intuitive basis of Frege's system; 3.2. Frege's system; 3.3. The theorem of infinity; 3.4. Criticisms of Frege's system; 3.5. The paradoxes; 3.6. Brouwer and intuitionism; 3.7. Poincare'snotion of im predicative definition; 3.8. Russell's principle of vicious circle; 3.9. The logical paradoxes and the semantic paradoxes; Chapter 4. The Theory of Types; 4.1. Quantifying predicate letters |
4.2. Predicative type theory4.3. The development of mathematics in PT; 4.4. The system TT; 4.5. Criticisms of type theory as a foundation for mathematics; 4.6. The system ST; 4.7. Type theory and first-order logic; Chapter 5. Zermelo-Fraenkel Set Theory; 5.1. Formalization of ZF; 5.2. The completing axioms; 5.3. Relations, functions, and simple recursion; 5.4. The axiom of choice; 5.5. The continuum hypothesis; |
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