Sets, Functions, Measures. / Volume 1, : Fundamentals of Set and Number Theory / / Timofey V. Rodionov, Valeriy K. Zakharov.
This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for re...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2018] ©2018 |
Year of Publication: | 2018 |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
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Physical Description: | 1 online resource (XVIII, 428 p.) |
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Zakharov, Valeriy K., author. aut http://id.loc.gov/vocabulary/relators/aut Sets, Functions, Measures. Volume 1, Fundamentals of Set and Number Theory / Timofey V. Rodionov, Valeriy K. Zakharov. Berlin ; Boston : De Gruyter, [2018] ©2018 1 online resource (XVIII, 428 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 68/1 Frontmatter -- Contents -- Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory -- Preface -- 1 Fundamentals of the theory of classes, sets, and numbers -- A Characterization of all natural models of Neumann – Bernays – Gödel and Zermelo – Fraenkel set theories -- B Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory -- C Compactness theorem for generalized second-order language -- Index of terms -- Index of notations -- Bibliography restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language 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 28. Feb 2023) Klasse ‹Mathematik›. Mathematische Logik. Mengenlehre. Zahlensystem. MATHEMATICS / Set Theory. bisacsh Rodionov, Timofey V., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1 9783110762488 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 9783110719550 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English 9783110604252 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 9783110603255 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English 9783110604191 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 9783110603194 ZDB-23-DMA EPUB 9783110550214 print 9783110550085 https://doi.org/10.1515/9783110550948 https://www.degruyter.com/isbn/9783110550948 Cover https://www.degruyter.com/document/cover/isbn/9783110550948/original |
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English |
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author |
Zakharov, Valeriy K., Zakharov, Valeriy K., Rodionov, Timofey V., |
spellingShingle |
Zakharov, Valeriy K., Zakharov, Valeriy K., Rodionov, Timofey V., Sets, Functions, Measures. De Gruyter Studies in Mathematics , Frontmatter -- Contents -- Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory -- Preface -- 1 Fundamentals of the theory of classes, sets, and numbers -- A Characterization of all natural models of Neumann – Bernays – Gödel and Zermelo – Fraenkel set theories -- B Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory -- C Compactness theorem for generalized second-order language -- Index of terms -- Index of notations -- Bibliography |
author_facet |
Zakharov, Valeriy K., Zakharov, Valeriy K., Rodionov, Timofey V., Rodionov, Timofey V., Rodionov, Timofey V., |
author_variant |
v k z vk vkz v k z vk vkz t v r tv tvr |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Rodionov, Timofey V., Rodionov, Timofey V., |
author2_variant |
t v r tv tvr |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Zakharov, Valeriy K., |
title |
Sets, Functions, Measures. |
title_full |
Sets, Functions, Measures. Volume 1, Fundamentals of Set and Number Theory / Timofey V. Rodionov, Valeriy K. Zakharov. |
title_fullStr |
Sets, Functions, Measures. Volume 1, Fundamentals of Set and Number Theory / Timofey V. Rodionov, Valeriy K. Zakharov. |
title_full_unstemmed |
Sets, Functions, Measures. Volume 1, Fundamentals of Set and Number Theory / Timofey V. Rodionov, Valeriy K. Zakharov. |
title_auth |
Sets, Functions, Measures. |
title_alt |
Frontmatter -- Contents -- Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory -- Preface -- 1 Fundamentals of the theory of classes, sets, and numbers -- A Characterization of all natural models of Neumann – Bernays – Gödel and Zermelo – Fraenkel set theories -- B Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory -- C Compactness theorem for generalized second-order language -- Index of terms -- Index of notations -- Bibliography |
title_new |
Sets, Functions, Measures. |
title_sort |
sets, functions, measures. fundamentals of set and number theory / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2018 |
physical |
1 online resource (XVIII, 428 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory -- Preface -- 1 Fundamentals of the theory of classes, sets, and numbers -- A Characterization of all natural models of Neumann – Bernays – Gödel and Zermelo – Fraenkel set theories -- B Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory -- C Compactness theorem for generalized second-order language -- Index of terms -- Index of notations -- Bibliography |
isbn |
9783110550948 9783110762488 9783110719550 9783110494938 9783110604252 9783110603255 9783110604191 9783110603194 9783110550214 9783110550085 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110550948 https://www.degruyter.com/isbn/9783110550948 https://www.degruyter.com/document/cover/isbn/9783110550948/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110550948 |
oclc_num |
1024006444 |
work_keys_str_mv |
AT zakharovvaleriyk setsfunctionsmeasuresvolume1 AT rodionovtimofeyv setsfunctionsmeasuresvolume1 |
status_str |
n |
ids_txt_mv |
(DE-B1597)482589 (OCoLC)1024006444 |
carrierType_str_mv |
cr |
title_part_txt |
Fundamentals of Set and Number Theory / |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 |
is_hierarchy_title |
Sets, Functions, Measures. |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1 |
author2_original_writing_str_mv |
noLinkedField noLinkedField |
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1806144451019538432 |
fullrecord |
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