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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)

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
Creator
Subject
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 first-order 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 self-study.--
Member of
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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-60231-8
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
The Setting -- First-Order 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 -- Silver-Like Forcing Notions -- Miller Forcing -- Mathias Forcing -- How Many Ramsey Ultrafilters Exist? -- Combinatorial Properties of Sets of Partitions -- Suite
Control code
978-3-319-60231-8
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, 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
9783319602318
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-60231-8
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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-60231-8
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
The Setting -- First-Order 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 -- Silver-Like Forcing Notions -- Miller Forcing -- Mathias Forcing -- How Many Ramsey Ultrafilters Exist? -- Combinatorial Properties of Sets of Partitions -- Suite
Control code
978-3-319-60231-8
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, 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
9783319602318
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-60231-8
Other physical details
20 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1017736581

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