000 | 04152nam a22005775i 4500 | ||
---|---|---|---|
001 | 978-3-540-34268-7 | ||
003 | DE-He213 | ||
005 | 20190213151648.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2006 gw | s |||| 0|eng d | ||
020 |
_a9783540342687 _9978-3-540-34268-7 |
||
024 | 7 |
_a10.1007/11601562 _2doi |
|
050 | 4 | _aQA8.9-10.3 | |
072 | 7 |
_aPBC _2bicssc |
|
072 | 7 |
_aMAT018000 _2bisacsh |
|
072 | 7 |
_aPBC _2thema |
|
072 | 7 |
_aPBCD _2thema |
|
082 | 0 | 4 |
_a511.3 _223 |
100 | 1 |
_aHerrlich, Horst. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aAxiom of Choice _h[electronic resource] / _cby Horst Herrlich. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006. |
|
300 |
_aXIV, 198 p. 1 illus. _bonline resource. |
||
336 |
_atext _btxt _2rdacontent |
||
337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
||
347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1876 |
|
505 | 0 | _aOrigins: 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). | |
520 | _aAC, 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. | ||
650 | 0 | _aLogic, Symbolic and mathematical. | |
650 | 0 | _aAlgebra. | |
650 | 0 | _aFunctional analysis. | |
650 | 0 | _aMathematics. | |
650 | 0 | _aCombinatorics. | |
650 | 0 | _aTopology. | |
650 | 1 | 4 |
_aMathematical Logic and Foundations. _0http://scigraph.springernature.com/things/product-market-codes/M24005 |
650 | 2 | 4 |
_aGeneral Algebraic Systems. _0http://scigraph.springernature.com/things/product-market-codes/M1106X |
650 | 2 | 4 |
_aFunctional Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M12066 |
650 | 2 | 4 |
_aGame Theory, Economics, Social and Behav. Sciences. _0http://scigraph.springernature.com/things/product-market-codes/M13011 |
650 | 2 | 4 |
_aCombinatorics. _0http://scigraph.springernature.com/things/product-market-codes/M29010 |
650 | 2 | 4 |
_aTopology. _0http://scigraph.springernature.com/things/product-market-codes/M28000 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540819066 |
776 | 0 | 8 |
_iPrinted edition: _z9783540309895 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1876 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/11601562 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c11454 _d11454 |