The Resource Axiom of Choice, by Horst Herrlich, (electronic resource)

Axiom of Choice, by Horst Herrlich, (electronic resource)

Label
Axiom of Choice
Title
Axiom of Choice
Statement of responsibility
by Horst Herrlich
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC). Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games). Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness). Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory
Member of
Is Subseries of
http://library.link/vocab/creatorName
Herrlich, Horst
Dewey number
511.3
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
-cvpvfM-8c8
Image bit depth
0
Language note
English
LC call number
QA8.9-10.3
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Lecture Notes in Mathematics,
Series volume
1876
http://library.link/vocab/subjectName
  • Logic, Symbolic and mathematical
  • Algebra
  • Functional analysis
  • Mathematics
  • Combinatorics
  • Topology
  • Mathematical Logic and Foundations
  • General Algebraic Systems
  • Functional Analysis
  • Game Theory, Economics, Social and Behav. Sciences
  • Combinatorics
  • Topology
Label
Axiom of Choice, by Horst Herrlich, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
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
Origins: Hilbert's First Problem -- Choice Principles: Some Equivalents to the Axiom of Choice, Some Concepts Related to the Axiom of Choice -- Elementary Observations: Hidden Choice, Unnecessary Choice, Concepts Split Up: Compactness -- Disasters without Choice: Finiteness, Disasters in Cardinal Arithmetic, Disasters in Order Theory, Disasters in Algebra I: Vector Spaces, Disasters in Algebra II: Categories, Disasters in Elementary Analysis: The Reals and Continuity, Disasters in Topology I: Countable Sums, Disasters in Topology II: Products (The Tychonoff and the Cech-Stone Theorem), Disasters in Topology III: Function Spaces (The Ascoli Theorem), Disasters in Topology IV: The Baire Category Theorem, Disasters in Graph Theory: Coloring Problems -- Disasters with Choice: Disasters in Elementary Analysis, Disasters in Geometry: Paradoxical Decompositions -- Disasters either way: Disasters in Game Theory -- Beauty without Choice: Lindelöf = Compact, Measurability (The Axiom of Determinateness)
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (XIV, 194 p. Also available online.)
File format
multiple file formats
Form of item
online
Isbn
9786610625789
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/11601562
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000232744
  • (DE-He213)978-3-540-34268-7
  • (SSID)ssj0000108244
  • (PQKBManifestationID)11145230
  • (PQKBTitleCode)TC0000108244
  • (PQKBWorkID)10044726
  • (PQKB)11575194
  • (MiAaPQ)EBC3036438
  • (EXLCZ)991000000000232744
Label
Axiom of Choice, by Horst Herrlich, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
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
Origins: Hilbert's First Problem -- Choice Principles: Some Equivalents to the Axiom of Choice, Some Concepts Related to the Axiom of Choice -- Elementary Observations: Hidden Choice, Unnecessary Choice, Concepts Split Up: Compactness -- Disasters without Choice: Finiteness, Disasters in Cardinal Arithmetic, Disasters in Order Theory, Disasters in Algebra I: Vector Spaces, Disasters in Algebra II: Categories, Disasters in Elementary Analysis: The Reals and Continuity, Disasters in Topology I: Countable Sums, Disasters in Topology II: Products (The Tychonoff and the Cech-Stone Theorem), Disasters in Topology III: Function Spaces (The Ascoli Theorem), Disasters in Topology IV: The Baire Category Theorem, Disasters in Graph Theory: Coloring Problems -- Disasters with Choice: Disasters in Elementary Analysis, Disasters in Geometry: Paradoxical Decompositions -- Disasters either way: Disasters in Game Theory -- Beauty without Choice: Lindelöf = Compact, Measurability (The Axiom of Determinateness)
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (XIV, 194 p. Also available online.)
File format
multiple file formats
Form of item
online
Isbn
9786610625789
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/11601562
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000232744
  • (DE-He213)978-3-540-34268-7
  • (SSID)ssj0000108244
  • (PQKBManifestationID)11145230
  • (PQKBTitleCode)TC0000108244
  • (PQKBWorkID)10044726
  • (PQKB)11575194
  • (MiAaPQ)EBC3036438
  • (EXLCZ)991000000000232744

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