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Can Mathematics Be Proved Consistent? [[electronic resource] ] : Gödel's Shorthand Notes & Lectures on Incompleteness / / by Jan von Plato
| Can Mathematics Be Proved Consistent? [[electronic resource] ] : Gödel's Shorthand Notes & Lectures on Incompleteness / / by Jan von Plato |
| Autore | von Plato Jan |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (IX, 263 p.) |
| Disciplina | 511.3 |
| Collana | Sources and Studies in the History of Mathematics and Physical Sciences |
| Soggetto topico |
Mathematics
History Mathematical logic History of Mathematical Sciences Mathematical Logic and Foundations |
| ISBN | 3-030-50876-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I. Gödel's Steps Toward Incompleteness -- II. The Saved Sources on Incompleteness -- III. The Shorthand Notebooks -- IV. The Typewritten Manuscripts -- V. Lectures and Seminars on Incompleteness -- Index -- References. |
| Record Nr. | UNISA-996418266103316 |
von Plato Jan
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Can Mathematics Be Proved Consistent? : Gödel's Shorthand Notes & Lectures on Incompleteness / / by Jan von Plato
| Can Mathematics Be Proved Consistent? : Gödel's Shorthand Notes & Lectures on Incompleteness / / by Jan von Plato |
| Autore | von Plato Jan |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (IX, 263 p.) |
| Disciplina | 511.3 |
| Collana | Sources and Studies in the History of Mathematics and Physical Sciences |
| Soggetto topico |
Mathematics
History Mathematical logic History of Mathematical Sciences Mathematical Logic and Foundations |
| ISBN | 3-030-50876-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I. Gödel's Steps Toward Incompleteness -- II. The Saved Sources on Incompleteness -- III. The Shorthand Notebooks -- IV. The Typewritten Manuscripts -- V. Lectures and Seminars on Incompleteness -- Index -- References. |
| Record Nr. | UNINA-9910484663003321 |
|
von Plato Jan
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Portrait of Young Gödel : Education, First Steps in Logic, the Problem of Completeness
| Portrait of Young Gödel : Education, First Steps in Logic, the Problem of Completeness |
| Autore | von Plato Jan |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing AG, , 2024 |
| Descrizione fisica | 1 online resource (314 pages) |
| Collana | Vienna Circle Institute Library |
| ISBN | 3-031-51971-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- CONTENTS -- PREFACE -- Part I At high school and university -- 1. At high school -- 1.1. High school extraordinary -- 1.2. The activity of the human mind -- 1.3. Molecular theory -- 1.4. Gödel's esoteric side -- 2. At university: from physics to mathematics -- 2.1. The physics student -- 2.2. Mathematics and philosophy -- Part II First steps in logic -- 1. First encounters with foundational problems -- 2. The Weber-Heft -- 3. The Übungsheft Logik -- 3.1. Exercise in constitutional analysis -- 3.2. Formal derivations in higher-order arithmetic and set theory -- 3.3. Beautiful syntax trees and other diversions -- 3.4. Summary overview of the Übungsheft -- 4. Punktmengenlehre -- 4.1. Hilbert's geometry -- 4.2. Hausdorff's point set topology -- Part III The problem of completeness -- 1. From Carnap's exercises to the problem of completeness -- 2. Dissertation draft -- 2.1. Generality -- 2.2. First-order logic -- 2.3. The proof of completeness -- 3. Completeness of the axioms of the narrower function calculus -- 4. Lectures and seminars on completeness -- 5. Anticipations of incompleteness -- Part IV The shorthand notebooks -- 1. The Weber-Heft -- 2. Übungsheft Logik: Formal derivations -- 3. Punktmengenlehre: Hilbert's geometry -- 4. Punktmengenlehre and Übungsheft: Set theory and topology -- 5. Dissertation draft -- 6. Completeness of the axioms of the narrower function calculus -- Part V Lectures and seminars on completeness -- 1. On the completeness of the axioms of the logical function calculus -- 2. Lecture in Königsberg, 6 September 1930 -- 3. Lecture in Vienna -- 4. Report on Gödel's work -- Completeness of the function calculus -- INDEX OF NAMES IN THE GÖDEL PAPERS -- REFERENCES FOR PARTS I-III. |
| Record Nr. | UNINA-9910831011603321 |
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von Plato Jan
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| Cham : , : Springer International Publishing AG, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Saved from the Cellar : Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics / / by Jan von Plato
| Saved from the Cellar : Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics / / by Jan von Plato |
| Autore | von Plato Jan |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (X, 315 p. 9 illus.) |
| Disciplina | 510.9 |
| Collana | Sources and Studies in the History of Mathematics and Physical Sciences |
| Soggetto topico |
Mathematics
History Mathematical logic History of Mathematical Sciences Mathematical Logic and Foundations |
| ISBN | 3-319-42120-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I: A Sketch of Gentzen's Life and Work -- 1. Overture -- 2. Gentzen's years of study -- Dr. Gentzen's arduous years in Nazi Germany -- 4. The scientific accomplishments -- 5. Loose ends -- 6. Gentzen's genuis -- Part II: Overview of the Shorthand Notes -- 1. Gentzen's series of stenographic manuscripts -- 2. The items in this collection -- Practical remarks on the manuscripts -- Manuscript illustrations -- The German alphabet in Latin, Sutterlin, and Fraktur Type -- Bibliography for parts I and II -- Index of names for Parts I and II -- Part III: The Original Writings -- 1. Reduction of number-theoretic problems to predicate logic -- 2. Replacement of functions by predicates -- 3. The formation of abstract concepts -- 4. Five different forms of natural calculi -- 5. Formal conception of correctness in arithmetic I -- 6. Investigations into logical inferences -- 7. Reduction of classical to intuitionistic logic -- 8. CV of the candidate Gerhard Gentzen.-0 9. Letters to Heyting -- 10. Formal conception of correctness in arithmetic II -- 11. Proof theory of number theory -- 12. Consistency of artihmetic, for publication -- 13. Correspondence with Paul Bernays -- 14. Forms of type theory -- 15. Predicate logic -- 16. Propositional logic -- 17. Foundational research in mathematics -- Table of cross-references in the Gentzen papers -- Index of names in the Gentzen papers -- Index of subjects in the Gentzen papers. |
| Record Nr. | UNINA-9910254305503321 |
|
von Plato Jan
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||