Two Applications of Logic to Mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2015]
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| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher’s Web site, viewed June 24 2015) |
| Beschreibung: | 1 online resource (152pages) illustrations |
| ISBN: | 9781400871346 |
| DOI: | 10.1515/9781400871346 |
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| 505 | 8 | |a Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean- valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905 | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Takeuti, Gaisi |
| author_facet | Takeuti, Gaisi |
| author_role | aut |
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| contents | Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean- valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905 |
| ctrlnum | (OCoLC)1165529730 (DE-599)BVBBV043016361 |
| 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 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400871346 |
| format | Electronic eBook |
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| spelling | Takeuti, Gaisi aut Two Applications of Logic to Mathematics Gaisi Takeuti Princeton, N.J. Princeton University Press [2015] © 2015 1 online resource (152pages) illustrations txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher’s Web site, viewed June 24 2015) Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean- valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905 In English Algebra, Boolean Logic, Symbolic and mathematical Mathematik MATHEMATICS / Logic bisacsh Boolesche Algebra (DE-588)4146280-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Analysis (DE-588)4001865-9 s Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Boolesche Algebra (DE-588)4146280-4 s 2\p DE-604 https://doi.org/10.1515/9781400871346 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 |
| spellingShingle | Takeuti, Gaisi Two Applications of Logic to Mathematics Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean- valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905 Algebra, Boolean Logic, Symbolic and mathematical Mathematik MATHEMATICS / Logic bisacsh Boolesche Algebra (DE-588)4146280-4 gnd Analysis (DE-588)4001865-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4146280-4 (DE-588)4001865-9 (DE-588)4037951-6 |
| title | Two Applications of Logic to Mathematics |
| title_auth | Two Applications of Logic to Mathematics |
| title_exact_search | Two Applications of Logic to Mathematics |
| title_full | Two Applications of Logic to Mathematics Gaisi Takeuti |
| title_fullStr | Two Applications of Logic to Mathematics Gaisi Takeuti |
| title_full_unstemmed | Two Applications of Logic to Mathematics Gaisi Takeuti |
| title_short | Two Applications of Logic to Mathematics |
| title_sort | two applications of logic to mathematics |
| topic | Algebra, Boolean Logic, Symbolic and mathematical Mathematik MATHEMATICS / Logic bisacsh Boolesche Algebra (DE-588)4146280-4 gnd Analysis (DE-588)4001865-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Algebra, Boolean Logic, Symbolic and mathematical Mathematik MATHEMATICS / Logic Boolesche Algebra Analysis Mathematische Logik |
| url | https://doi.org/10.1515/9781400871346 |
| work_keys_str_mv | AT takeutigaisi twoapplicationsoflogictomathematics |