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Extending ZFC - Two Contenders

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  • Eric Cordian
    https://www.simonsfoundation.org/quanta/20131126-to-settle-infinity-question-a-new-law-of-logic/ The decades-long quest for a more complete axiomatic system,
    Message 1 of 1 , Nov 27, 2013
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      The decades-long quest for a more complete axiomatic system, one that could settle the infinity question and plug many of the other holes in mathematics at the same time, has arrived at a crossroads. During a recent meeting at Harvard organized by Koellner, scholars largely agreed upon two main contenders for additions to ZFC: forcing axioms and the inner-model axiom “V=ultimate L.”
      “If forcing axioms are right, then the continuum hypothesis is false,” Koellner said. “And if the inner-model axiom is right, then the continuum hypothesis is true. You go through a whole list of issues in other fields, and the forcing axioms will answer those questions one way, and ultimate L will answer them a different way.”


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