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  • This is a survey paper which discusses the impact of large cardinals on provability of the Continuum Hypothesis (CH). It was Gödel who first suggested that perhaps %22strong axioms of infinity%22 (large cardinals) could decide interesting set-theoretical statements independent over ZFC, such as CH. This hope proved largely unfounded for CH - one can show that virtually all large cardinals defined so far do not affect the status of CH. It seems to be an inherent feature of large cardinals that they do not determine properties of sets low in the cumulative hierarchy if such properties can be forced to hold or fail by small forcings.
  • This is a survey paper which discusses the impact of large cardinals on provability of the Continuum Hypothesis (CH). It was Gödel who first suggested that perhaps %22strong axioms of infinity%22 (large cardinals) could decide interesting set-theoretical statements independent over ZFC, such as CH. This hope proved largely unfounded for CH - one can show that virtually all large cardinals defined so far do not affect the status of CH. It seems to be an inherent feature of large cardinals that they do not determine properties of sets low in the cumulative hierarchy if such properties can be forced to hold or fail by small forcings. (en)
Title
  • Large Cardinals and the Continuum Hypothesis
  • Large Cardinals and the Continuum Hypothesis (en)
skos:prefLabel
  • Large Cardinals and the Continuum Hypothesis
  • Large Cardinals and the Continuum Hypothesis (en)
skos:notation
  • RIV/00216208:11210/13:10173337!RIV14-MSM-11210___
http://linked.open...avai/riv/aktivita
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  • I
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  • 2
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  • 84309
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11210/13:10173337
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  • forcing; large cardinals (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [587CB6E2EE25]
http://linked.open...i/riv/nazevZdroje
  • Acta Universitatis Carolinae. Philosophica et Historica
http://linked.open...in/vavai/riv/obor
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http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2010
http://linked.open...iv/tvurceVysledku
  • Honzík, Radek
issn
  • 0567-8293
number of pages
http://localhost/t...ganizacniJednotka
  • 11210
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