Two Applications of Logic to Mathematics
()
Currently unavailable
Currently unavailable
About this ebook
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.
Related to Two Applications of Logic to Mathematics
Titles in the series (6)
Engineers of Happy Land: Technology and Nationalism in a Colony Rating: 5 out of 5 stars5/5The Interpretation of Quantum Mechanics Rating: 3 out of 5 stars3/5Regulating the Social: The Welfare State and Local Politics in Imperial Germany Rating: 0 out of 5 stars0 ratingsSocial Bodies: Science, Reproduction, and Italian Modernity Rating: 5 out of 5 stars5/5Gibeon, Where the Sun Stood Still: The Discovery of the Biblical City Rating: 4 out of 5 stars4/5Colonialism and Revolution in the Middle East: Social and Cultural Origins of Egypt's Urabi Movement Rating: 4 out of 5 stars4/5
Related ebooks
Theory of Charges: A Study of Finitely Additive Measures Rating: 0 out of 5 stars0 ratingsNumber Theory Rating: 0 out of 5 stars0 ratingsA Graduate Course in Probability Rating: 5 out of 5 stars5/5Probability and Mathematical Statistics: An Introduction Rating: 3 out of 5 stars3/5Mathematical Techniques of Applied Probability: Discrete Time Models: Basic Theory Rating: 5 out of 5 stars5/5Principles of Combinatorics Rating: 0 out of 5 stars0 ratingsLie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34 Rating: 0 out of 5 stars0 ratingsIntroduction to the Theory and Application of Differential Equations with Deviating Arguments Rating: 0 out of 5 stars0 ratingsFunctional Analysis Rating: 4 out of 5 stars4/5Functional Equations in Probability Theory Rating: 0 out of 5 stars0 ratingsDifferential Equations in Abstract Spaces Rating: 0 out of 5 stars0 ratingsQuantum Mechanics in Hilbert Space Rating: 0 out of 5 stars0 ratingsStochastic Calculus and Stochastic Models Rating: 0 out of 5 stars0 ratingsAn Introduction to Complex Analysis in Several Variables Rating: 0 out of 5 stars0 ratingsFundamentals of the Theory of Operator Algebras. V1: Elementary Theory Rating: 0 out of 5 stars0 ratingsApplications of Functional Analysis and Operator Theory Rating: 0 out of 5 stars0 ratingsRandom Integral Equations Rating: 0 out of 5 stars0 ratingsClassical Dynamics of Particles and Systems Rating: 5 out of 5 stars5/5Elastic Waves in the Earth Rating: 0 out of 5 stars0 ratingsThe Lambda Calculus: Its Syntax and Semantics Rating: 5 out of 5 stars5/5Mathematical Methods: Linear Algebra / Normed Spaces / Distributions / Integration Rating: 0 out of 5 stars0 ratingsGroups - Modular Mathematics Series Rating: 0 out of 5 stars0 ratingsAnalytic Theory of Global Bifurcation: An Introduction Rating: 0 out of 5 stars0 ratingsMartingale Limit Theory and Its Application Rating: 0 out of 5 stars0 ratingsLinear Models: A Mean Model Approach Rating: 0 out of 5 stars0 ratingsElementary Theory: Fundamentals of the Theory of Operator Algebras Rating: 0 out of 5 stars0 ratingsNonlinear Autonomous Oscillations: Analytical Theory Rating: 5 out of 5 stars5/5An Introduction to Group Representation Theory Rating: 0 out of 5 stars0 ratingsMathematical Analysis: A Special Course Rating: 0 out of 5 stars0 ratingsOperators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics Rating: 3 out of 5 stars3/5
Mathematics For You
Real Estate by the Numbers: A Complete Reference Guide to Deal Analysis Rating: 0 out of 5 stars0 ratingsMy Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5The Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5Standard Deviations: Flawed Assumptions, Tortured Data, and Other Ways to Lie with Statistics Rating: 4 out of 5 stars4/5Calculus Made Easy Rating: 4 out of 5 stars4/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game - Updated Edition Rating: 4 out of 5 stars4/5Precalculus: A Self-Teaching Guide Rating: 5 out of 5 stars5/5Algebra - The Very Basics Rating: 5 out of 5 stars5/5Flatland Rating: 4 out of 5 stars4/5The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics Rating: 3 out of 5 stars3/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsThe Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Geometry For Dummies Rating: 5 out of 5 stars5/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5Sneaky Math: A Graphic Primer with Projects Rating: 0 out of 5 stars0 ratingsGame Theory: A Simple Introduction Rating: 4 out of 5 stars4/5The Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5Relativity: The special and the general theory Rating: 5 out of 5 stars5/5How Not To Be Wrong | Summary Rating: 5 out of 5 stars5/5
Reviews for Two Applications of Logic to Mathematics
0 ratings0 reviews