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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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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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Buchbeschreibung Princeton University Press, United States, 2015. Paperback. Buchzustand: New. Reprint. 226 x 150 mm. Language: English . Brand New Book. 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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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. Buchnummer des Verkäufers AAH9780691610221

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Buchbeschreibung Princeton University Press, 2015. PAP. Buchzustand: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Buchnummer des Verkäufers IQ-9780691610221

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Buchbeschreibung Princeton University Press, 2015. PAP. Buchzustand: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Buchnummer des Verkäufers IQ-9780691610221

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Buchbeschreibung Princeton University Press, United States, 2015. Paperback. Buchzustand: New. Reprint. 226 x 150 mm. Language: English . Brand New Book. 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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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. Buchnummer des Verkäufers AAH9780691610221

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Buchbeschreibung Princeton University Press. Paperback. Buchzustand: New. This item is printed on demand. Paperback. 152 pages. Dimensions: 9.2in. x 6.1in. x 0.3in.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- Solovays 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 Peanos arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peanos arithmetic. In doing so, the author applies Gentzens 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. This item ships from La Vergne,TN. Paperback. Buchnummer des Verkäufers 9780691610221

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Buchbeschreibung Princeton Univ Pr, 2015. Paperback. Buchzustand: Brand New. reprint edition. 137 pages. 9.00x6.00x0.50 inches. In Stock. Buchnummer des Verkäufers x-0691610223

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Buchbeschreibung 2015. Paperback. Buchzustand: New. 157mm x 234mm x. Paperback. 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 pre.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 148 pages. 0.238. Buchnummer des Verkäufers 9780691610221

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Buchbeschreibung Princeton University Press, 2015. Paperback. Buchzustand: Used: Good. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. May not contain Access Codes or Supplements. Buy with confidence, excellent customer service!. Buchnummer des Verkäufers 0691610223

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