Forcing lightface definable well-orders without the CGH

David Aspero, Peter Holy, Philipp Luecke

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For any given uncountable cardinal \(\kappa\) with \(\kappa^{{<}\kappa}=\kappa\), we present a forcing that is \(<\kappa\)-directed closed, has the \(\kappa^+\)-c.c. and introduces a lightface definable well-order of \(H(\kappa^+)\). We use this to define a global iteration that does this for all such \(\kappa\) simultaneously and is capable of preserving the existence of many large cardinals in the universe.
Original languageEnglish
Pages (from-to)553–582
Number of pages30
JournalAnnals of Pure and Applied Logic
Issue number5
Early online date29 Dec 2014
Publication statusPublished - May 2015


  • Definable well-orders
  • Forcing
  • Large cardinals

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