The Resource Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (electronic resource)
Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (electronic resource)
Resource Information
The item Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (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 Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (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
 This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and firstorder logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for selfstudy.
 Language
 eng
 Edition
 2nd ed. 2017.
 Extent
 1 online resource (XVI, 594 pages)
 Contents

 The Setting
 FirstOrder Logic in a Nutshell
 Axioms of Set Theory
 Overture: Ramsey's Theorem
 Cardinal Relations in ZF Only
 Forms of Choice
 How to Make Two Balls from One
 Models of Set Theory with Atoms
 Thirteen Cardinals and Their Relations
 The Shattering Number Revisited
 Happy Families and Their Relatives
 Coda: A Dual Form of Ramsey’s Theorem
 The Idea of Forcing
 Martin's Axiom
 The Notion of Forcing
 Proving Unprovability
 Models in Which AC Fails
 Combining Forcing Notions
 Models in Which p=c
 Suslin’s Problem
 Properties of Forcing Extensions
 Cohen Forcing Revisited
 Sacks Forcing
 SilverLike Forcing Notions
 Miller Forcing
 Mathias Forcing
 How Many Ramsey Ultrafilters Exist?
 Combinatorial Properties of Sets of Partitions
 Suite
 Isbn
 9783319602318
 Label
 Combinatorial Set Theory : With a Gentle Introduction to Forcing
 Title
 Combinatorial Set Theory
 Title remainder
 With a Gentle Introduction to Forcing
 Statement of responsibility
 by Lorenz J. Halbeisen
 Language
 eng
 Summary
 This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and firstorder logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for selfstudy.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Halbeisen, Lorenz J
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Springer eBooks
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Mathematical logic
 Combinatorics
 Label
 Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (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
 The Setting  FirstOrder Logic in a Nutshell  Axioms of Set Theory  Overture: Ramsey's Theorem  Cardinal Relations in ZF Only  Forms of Choice  How to Make Two Balls from One  Models of Set Theory with Atoms  Thirteen Cardinals and Their Relations  The Shattering Number Revisited  Happy Families and Their Relatives  Coda: A Dual Form of Ramsey’s Theorem  The Idea of Forcing  Martin's Axiom  The Notion of Forcing  Proving Unprovability  Models in Which AC Fails  Combining Forcing Notions  Models in Which p=c  Suslin’s Problem  Properties of Forcing Extensions  Cohen Forcing Revisited  Sacks Forcing  SilverLike Forcing Notions  Miller Forcing  Mathias Forcing  How Many Ramsey Ultrafilters Exist?  Combinatorial Properties of Sets of Partitions  Suite
 Control code
 9783319602318
 Dimensions
 unknown
 Edition
 2nd ed. 2017.
 Extent
 1 online resource (XVI, 594 pages)
 File format
 multiple file formats
 Form of item

 online
 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
 9783319602318
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319602318
 Other physical details
 20 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1017736581
 Label
 Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (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
 The Setting  FirstOrder Logic in a Nutshell  Axioms of Set Theory  Overture: Ramsey's Theorem  Cardinal Relations in ZF Only  Forms of Choice  How to Make Two Balls from One  Models of Set Theory with Atoms  Thirteen Cardinals and Their Relations  The Shattering Number Revisited  Happy Families and Their Relatives  Coda: A Dual Form of Ramsey’s Theorem  The Idea of Forcing  Martin's Axiom  The Notion of Forcing  Proving Unprovability  Models in Which AC Fails  Combining Forcing Notions  Models in Which p=c  Suslin’s Problem  Properties of Forcing Extensions  Cohen Forcing Revisited  Sacks Forcing  SilverLike Forcing Notions  Miller Forcing  Mathias Forcing  How Many Ramsey Ultrafilters Exist?  Combinatorial Properties of Sets of Partitions  Suite
 Control code
 9783319602318
 Dimensions
 unknown
 Edition
 2nd ed. 2017.
 Extent
 1 online resource (XVI, 594 pages)
 File format
 multiple file formats
 Form of item

 online
 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
 9783319602318
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319602318
 Other physical details
 20 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1017736581
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/CombinatorialSetTheoryWithaGentle/dU8jcVXjS4Q/" 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/CombinatorialSetTheoryWithaGentle/dU8jcVXjS4Q/">Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (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>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/CombinatorialSetTheoryWithaGentle/dU8jcVXjS4Q/" 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/CombinatorialSetTheoryWithaGentle/dU8jcVXjS4Q/">Combinatorial Set Theory : With a Gentle Introduction to Forcing, by Lorenz J. Halbeisen, (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>