Two Applications of Logic to Mathematics

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.