skip to content
Combinatorial set theory : with a gentle introduction to forcing Preview this item
ClosePreview this item
Checking...

Combinatorial set theory : with a gentle introduction to forcing

Author: Lorenz J Halbeisen
Publisher: Cham, Switzerland : Springer, [2017]
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Lorenz J Halbeisen
ISBN: 9783319602318 3319602314 3319602306 9783319602301
OCLC Number: 1017736581
Description: 1 online resource.
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.
Series Title: Springer monographs in mathematics.
Responsibility: Lorenz J. Halbeisen.

Abstract:

This introduction to modern set theory opens the way to advanced current research. Coverage includes the axiom of choice and Ramsey theory, and a detailed explanation of the sophisticated technique  Read more...

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/1017736581> # Combinatorial set theory : with a gentle introduction to forcing
    a schema:Book, schema:CreativeWork, schema:MediaObject ;
    library:oclcnum "1017736581" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/sz> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/1056884895#Topic/combinatorial_set_theory> ; # Combinatorial set theory
    schema:about <http://experiment.worldcat.org/entity/work/data/1056884895#Topic/forcing_model_theory> ; # Forcing (Model theory)
    schema:about <http://experiment.worldcat.org/entity/work/data/1056884895#Topic/mathematics_general> ; # MATHEMATICS--General
    schema:about <http://dewey.info/class/511.322/e23/> ;
    schema:author <http://experiment.worldcat.org/entity/work/data/1056884895#Person/halbeisen_lorenz_j> ; # Lorenz J. Halbeisen
    schema:bookEdition "Second edition." ;
    schema:bookFormat schema:EBook ;
    schema:datePublished "2017" ;
    schema:description "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."@en ;
    schema:description "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 Suslins 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 Shelahs astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, 㯭mbinatorial Set Theory穬l 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." ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/1056884895> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/1056884895#Series/springer_monographs_in_mathematics> ; # Springer monographs in mathematics.
    schema:isSimilarTo <http://worldcat.org/entity/work/data/1056884895#CreativeWork/> ;
    schema:name "Combinatorial set theory : with a gentle introduction to forcing"@en ;
    schema:productID "1017736581" ;
    schema:url <https://link.springer.com/openurl?genre=book&isbn=978-3-319-60230-1> ;
    schema:url <http://link.springer.com/10.1007/978-3-319-60231-8> ;
    schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1665770> ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/10.1007/978-3-319-60231-8> ;
    schema:url <https://grinnell.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-60231-8> ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/book/10.1007/978-3-319-60231-8> ;
    schema:url <http://dx.doi.org/10.1007/978-3-319-60231-8> ;
    schema:url <http://proxy.ohiolink.edu:9099/login?url=http://link.springer.com/10.1007/978-3-319-60231-8> ;
    schema:url <http://rave.ohiolink.edu/ebooks/ebc/9783319602318> ;
    schema:workExample <http://dx.doi.org/10.1007/978-3-319-60231-8> ;
    schema:workExample <http://worldcat.org/isbn/9783319602318> ;
    schema:workExample <http://worldcat.org/isbn/9783319602301> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/1017736581> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/1056884895#Person/halbeisen_lorenz_j> # Lorenz J. Halbeisen
    a schema:Person ;
    schema:familyName "Halbeisen" ;
    schema:givenName "Lorenz J." ;
    schema:name "Lorenz J. Halbeisen" ;
    .

<http://experiment.worldcat.org/entity/work/data/1056884895#Series/springer_monographs_in_mathematics> # Springer monographs in mathematics.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1017736581> ; # Combinatorial set theory : with a gentle introduction to forcing
    schema:name "Springer monographs in mathematics." ;
    schema:name "Springer monographs in mathematics" ;
    .

<http://experiment.worldcat.org/entity/work/data/1056884895#Topic/combinatorial_set_theory> # Combinatorial set theory
    a schema:Intangible ;
    schema:name "Combinatorial set theory"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1056884895#Topic/forcing_model_theory> # Forcing (Model theory)
    a schema:Intangible ;
    schema:name "Forcing (Model theory)"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1056884895#Topic/mathematics_general> # MATHEMATICS--General
    a schema:Intangible ;
    schema:name "MATHEMATICS--General"@en ;
    .

<http://rave.ohiolink.edu/ebooks/ebc/9783319602318>
    rdfs:comment "Connect to resource" ;
    .

<http://worldcat.org/entity/work/data/1056884895#CreativeWork/>
    a schema:CreativeWork ;
    schema:description "Printed edition:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/1017736581> ; # Combinatorial set theory : with a gentle introduction to forcing
    .

<http://worldcat.org/isbn/9783319602301>
    a schema:ProductModel ;
    schema:isbn "3319602306" ;
    schema:isbn "9783319602301" ;
    .

<http://worldcat.org/isbn/9783319602318>
    a schema:ProductModel ;
    schema:isbn "3319602314" ;
    schema:isbn "9783319602318" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.