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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.\u003cbr\u003e\u003cbr\u003e 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.\u003cbr\u003e\u003cbr\u003eOriginally published in 1978.\u003cbr\u003e\u003cbr\u003eThe \u003cb\u003ePrinceton Legacy Library\u003c\/b\u003e 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. 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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.\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":52641077952879,"sku":"9780691621401","price":251.23,"currency_code":"BRL","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0921\/9384\/9711\/files\/0691621403.jpg?v=1770405749"},{"product_id":"estimates-of-the-neumann-problem-mn-19-volume-19","title":"Estimates of the Neumann Problem. (MN-19), Volume 19","description":"\u003cp\u003eThe ?¯ Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. 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