The Resource Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource)
Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource)
Resource Information
The item Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenthcentury mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the DedekindPeano axioms and ends with the construction of the real numbers. The core CantorDedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a yearlong course at the upperundergraduate level. For shorter onesemester or onequarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via selfstudy
 Language
 eng
 Extent
 XV, 444 pages 17 illustrations
 Contents

 1 Preliminaries: Sets, Relations, and Functions
 Part I Dedekind: Numbers
 2 The DedekindPeano Axioms
 3 Dedekind's Theory of the Continuum
 4 Postscript I: What Exactly Are the Natural Numbers?
 Part II Cantor: Cardinals, Order, and Ordinals
 5 Cardinals: Finite, Countable, and Uncountable
 6 Cardinal Arithmetic and the Cantor Set
 7 Orders and Order Types
 8 Dense and Complete Orders
 9 WellOrders and Ordinals
 10 Alephs, Cofinality, and the Axiom of Choice
 11 Posets, Zorn's Lemma, Ranks, and Trees
 12 Postscript II: Infinitary Combinatorics
 Part III Real Point Sets
 13 Interval Trees and Generalized Cantor Sets
 14 Real Sets and Functions
 15 The HeineBorel and Baire Category Theorems
 16 CantorBendixson Analysis of Countable Closed Sets
 17 Brouwer's Theorem and Sierpinski's Theorem
 18 Borel and Analytic Sets
 19 Postscript III: Measurability and Projective Sets
 Part IV Paradoxes and Axioms
 20 Paradoxes and Resolutions
 21 ZermeloFraenkel System and von Neumann Ordinals
 22 Postscript IV: Landmarks of Modern Set Theory
 Appendices
 A Proofs of Uncountability of the Reals
 B Existence of Lebesgue Measure
 C List of ZF Axioms
 References
 List of Symbols and Notations
 Index
 Isbn
 9781461488545
 Label
 Set Theory : With an Introduction to Real Point Sets
 Title
 Set Theory
 Title remainder
 With an Introduction to Real Point Sets
 Statement of responsibility
 by Abhijit Dasgupta
 Language
 eng
 Summary
 What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenthcentury mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the DedekindPeano axioms and ends with the construction of the real numbers. The core CantorDedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a yearlong course at the upperundergraduate level. For shorter onesemester or onequarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via selfstudy
 Cataloging source
 ITFiEUI
 http://library.link/vocab/creatorName
 Dasgupta, Abhijit
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Logic
 Algebra
 Global analysis (Mathematics)
 Logic, Symbolic and mathematical
 Topology
 Label
 Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 Preliminaries: Sets, Relations, and Functions  Part I Dedekind: Numbers  2 The DedekindPeano Axioms  3 Dedekind's Theory of the Continuum  4 Postscript I: What Exactly Are the Natural Numbers?  Part II Cantor: Cardinals, Order, and Ordinals  5 Cardinals: Finite, Countable, and Uncountable  6 Cardinal Arithmetic and the Cantor Set  7 Orders and Order Types  8 Dense and Complete Orders  9 WellOrders and Ordinals  10 Alephs, Cofinality, and the Axiom of Choice  11 Posets, Zorn's Lemma, Ranks, and Trees  12 Postscript II: Infinitary Combinatorics  Part III Real Point Sets  13 Interval Trees and Generalized Cantor Sets  14 Real Sets and Functions  15 The HeineBorel and Baire Category Theorems  16 CantorBendixson Analysis of Countable Closed Sets  17 Brouwer's Theorem and Sierpinski's Theorem  18 Borel and Analytic Sets  19 Postscript III: Measurability and Projective Sets  Part IV Paradoxes and Axioms  20 Paradoxes and Resolutions  21 ZermeloFraenkel System and von Neumann Ordinals  22 Postscript IV: Landmarks of Modern Set Theory  Appendices  A Proofs of Uncountability of the Reals  B Existence of Lebesgue Measure  C List of ZF Axioms  References  List of Symbols and Notations  Index
 Control code
 9781461488545
 Dimensions
 unknown
 Extent
 XV, 444 pages 17 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781461488545
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9781461488545
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1058473896
 Label
 Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 Preliminaries: Sets, Relations, and Functions  Part I Dedekind: Numbers  2 The DedekindPeano Axioms  3 Dedekind's Theory of the Continuum  4 Postscript I: What Exactly Are the Natural Numbers?  Part II Cantor: Cardinals, Order, and Ordinals  5 Cardinals: Finite, Countable, and Uncountable  6 Cardinal Arithmetic and the Cantor Set  7 Orders and Order Types  8 Dense and Complete Orders  9 WellOrders and Ordinals  10 Alephs, Cofinality, and the Axiom of Choice  11 Posets, Zorn's Lemma, Ranks, and Trees  12 Postscript II: Infinitary Combinatorics  Part III Real Point Sets  13 Interval Trees and Generalized Cantor Sets  14 Real Sets and Functions  15 The HeineBorel and Baire Category Theorems  16 CantorBendixson Analysis of Countable Closed Sets  17 Brouwer's Theorem and Sierpinski's Theorem  18 Borel and Analytic Sets  19 Postscript III: Measurability and Projective Sets  Part IV Paradoxes and Axioms  20 Paradoxes and Resolutions  21 ZermeloFraenkel System and von Neumann Ordinals  22 Postscript IV: Landmarks of Modern Set Theory  Appendices  A Proofs of Uncountability of the Reals  B Existence of Lebesgue Measure  C List of ZF Axioms  References  List of Symbols and Notations  Index
 Control code
 9781461488545
 Dimensions
 unknown
 Extent
 XV, 444 pages 17 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781461488545
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9781461488545
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1058473896
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/SetTheoryWithanIntroductiontoRealPoint/v_OqrKSBhsk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/SetTheoryWithanIntroductiontoRealPoint/v_OqrKSBhsk/">Set Theory : With an Introduction to Real Point Sets, by Abhijit Dasgupta, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>