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The book explores the application of mathematical logic through set theory and proof theory. In the first part, it utilizes Scott-Solovay's Boolean-valued models to enhance analysis using complete Boolean algebras. The second part focuses on classical and complex analysis within Peano's arithmetic, demonstrating that any arithmetical theorem from analytic number theory can be derived in this framework. The author employs Gentzen's cut elimination theorem to support these findings, showcasing a more elegant approach to established mathematical results.
Nákup knihy
Two Applications of Logic to Mathematics, Gaisi Takeuti
- Jazyk
- Rok vydania
- 2016
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- Titul
- Two Applications of Logic to Mathematics
- Jazyk
- anglicky
- Autori
- Gaisi Takeuti
- Vydavateľ
- Princeton University Press
- Rok vydania
- 2016
- Väzba
- pevná
- Počet strán
- 148
- ISBN13
- 9780691638379
- Kategórie
- Matematika
- Anotácia
- The book explores the application of mathematical logic through set theory and proof theory. In the first part, it utilizes Scott-Solovay's Boolean-valued models to enhance analysis using complete Boolean algebras. The second part focuses on classical and complex analysis within Peano's arithmetic, demonstrating that any arithmetical theorem from analytic number theory can be derived in this framework. The author employs Gentzen's cut elimination theorem to support these findings, showcasing a more elegant approach to established mathematical results.