Two Applications of Logic to Mathematics / / Gaisi Takeuti.
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-...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2015] ©1978 |
Year of Publication: | 2015 |
Language: | English |
Series: | Publications of the Mathematical Society of Japan ;
1576 |
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Takeuti, Gaisi, author. aut http://id.loc.gov/vocabulary/relators/aut Two Applications of Logic to Mathematics / Gaisi Takeuti. Princeton, NJ : Princeton University Press, [2015] ©1978 1 online resource (148 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Publications of the Mathematical Society of Japan ; 1576 Frontmatter -- Preface -- Contents -- Introduction -- Part I. Boolean Valued Analysis -- Introduction -- Chapter 1. Boolean Valued Analysis Using Projection Algebras -- Chapter 2. Boolean Valued Analysis Using Measure Algebras -- References -- Part II. A Conservative Extension of Peano Arithmetic -- Introduction -- Chapter 1. Real Analysis -- Chapter 2. Complex Analysis -- References -- Index -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Algebra, Boolean. Logic, Symbolic and mathematical. MATHEMATICS / Logic. bisacsh Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 9783110426847 Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science 9783110413595 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691610221 https://doi.org/10.1515/9781400871346?locatt=mode:legacy https://www.degruyter.com/isbn/9781400871346 Cover https://www.degruyter.com/cover/covers/9781400871346.jpg |
language |
English |
format |
eBook |
author |
Takeuti, Gaisi, Takeuti, Gaisi, |
spellingShingle |
Takeuti, Gaisi, Takeuti, Gaisi, Two Applications of Logic to Mathematics / Publications of the Mathematical Society of Japan ; Frontmatter -- Preface -- Contents -- Introduction -- Part I. Boolean Valued Analysis -- Chapter 1. Boolean Valued Analysis Using Projection Algebras -- Chapter 2. Boolean Valued Analysis Using Measure Algebras -- References -- Part II. A Conservative Extension of Peano Arithmetic -- Chapter 1. Real Analysis -- Chapter 2. Complex Analysis -- Index -- Backmatter |
author_facet |
Takeuti, Gaisi, Takeuti, Gaisi, |
author_variant |
g t gt g t gt |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Takeuti, Gaisi, |
title |
Two Applications of Logic to Mathematics / |
title_full |
Two Applications of Logic to Mathematics / Gaisi Takeuti. |
title_fullStr |
Two Applications of Logic to Mathematics / Gaisi Takeuti. |
title_full_unstemmed |
Two Applications of Logic to Mathematics / Gaisi Takeuti. |
title_auth |
Two Applications of Logic to Mathematics / |
title_alt |
Frontmatter -- Preface -- Contents -- Introduction -- Part I. Boolean Valued Analysis -- Chapter 1. Boolean Valued Analysis Using Projection Algebras -- Chapter 2. Boolean Valued Analysis Using Measure Algebras -- References -- Part II. A Conservative Extension of Peano Arithmetic -- Chapter 1. Real Analysis -- Chapter 2. Complex Analysis -- Index -- Backmatter |
title_new |
Two Applications of Logic to Mathematics / |
title_sort |
two applications of logic to mathematics / |
series |
Publications of the Mathematical Society of Japan ; |
series2 |
Publications of the Mathematical Society of Japan ; |
publisher |
Princeton University Press, |
publishDate |
2015 |
physical |
1 online resource (148 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- Introduction -- Part I. Boolean Valued Analysis -- Chapter 1. Boolean Valued Analysis Using Projection Algebras -- Chapter 2. Boolean Valued Analysis Using Measure Algebras -- References -- Part II. A Conservative Extension of Peano Arithmetic -- Chapter 1. Real Analysis -- Chapter 2. Complex Analysis -- Index -- Backmatter |
isbn |
9781400871346 9783110426847 9783110413595 9783110665925 9783110442496 9780691610221 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA9 |
callnumber-sort |
QA 19 T26 |
url |
https://doi.org/10.1515/9781400871346?locatt=mode:legacy https://www.degruyter.com/isbn/9781400871346 https://www.degruyter.com/cover/covers/9781400871346.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511/.3 |
dewey-sort |
3511 13 |
dewey-raw |
511/.3 |
dewey-search |
511/.3 |
doi_str_mv |
10.1515/9781400871346?locatt=mode:legacy |
oclc_num |
903321560 |
work_keys_str_mv |
AT takeutigaisi twoapplicationsoflogictomathematics |
status_str |
n |
ids_txt_mv |
(DE-B1597)454492 (OCoLC)903321560 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Two Applications of Logic to Mathematics / |
container_title |
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 |
_version_ |
1806143624090484736 |
fullrecord |
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