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The Resource Axiom of Choice, by Horst Herrlich, (electronic resource)
Axiom of Choice, by Horst Herrlich, (electronic resource)
Resource Information
The item Axiom of Choice, by Horst Herrlich, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Axiom of Choice, by Horst Herrlich, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 AC, the axiom of choice, because of its nonconstructive 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
 Language

 eng
 eng
 Edition
 1st ed. 2006.
 Extent
 1 online resource (XIV, 194 p. Also available online.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 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 CechStone 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)
 Isbn
 9786610625789
 Label
 Axiom of Choice
 Title
 Axiom of Choice
 Statement of responsibility
 by Horst Herrlich
 Language

 eng
 eng
 Summary
 AC, the axiom of choice, because of its nonconstructive 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
 http://library.link/vocab/creatorName
 Herrlich, Horst
 Dewey number
 511.3
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 cvpvfM8c8
 Image bit depth
 0
 Language note
 English
 LC call number
 QA8.910.3
 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)
 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 CechStone 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
 (DEHe213)9783540342687
 (SSID)ssj0000108244
 (PQKBManifestationID)11145230
 (PQKBTitleCode)TC0000108244
 (PQKBWorkID)10044726
 (PQKB)11575194
 (MiAaPQ)EBC3036438
 (EXLCZ)991000000000232744
 Label
 Axiom of Choice, by Horst Herrlich, (electronic resource)
 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 CechStone 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
 (DEHe213)9783540342687
 (SSID)ssj0000108244
 (PQKBManifestationID)11145230
 (PQKBTitleCode)TC0000108244
 (PQKBWorkID)10044726
 (PQKB)11575194
 (MiAaPQ)EBC3036438
 (EXLCZ)991000000000232744
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
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