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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)

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
Creator
Contributor
Author
Subject
Language
eng
Summary
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century 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 Dedekind--Peano axioms and ends with the construction of the real numbers. The core Cantor--Dedekind 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 year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter 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 self-study
Member of
Cataloging source
IT-FiEUI
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)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4614-8854-5
Instantiates
Publication
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 Dedekind--Peano 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 Well-Orders 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 Heine--Borel and Baire Category Theorems -- 16 Cantor--Bendixson 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 Zermelo--Fraenkel 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
978-1-4614-8854-5
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, non-commercial 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
10.1007/978-1-4614-8854-5
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)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4614-8854-5
Publication
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 Dedekind--Peano 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 Well-Orders 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 Heine--Borel and Baire Category Theorems -- 16 Cantor--Bendixson 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 Zermelo--Fraenkel 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
978-1-4614-8854-5
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, non-commercial 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
10.1007/978-1-4614-8854-5
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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