Forcing lightface definable well-orders without the CGH

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Abstract

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.

Details

Original language English 553–582 30 Annals of Pure and Applied Logic 166 5 29 Dec 2014 https://doi.org/10.1016/j.apal.2014.11.010 Published - May 2015 Yes

Research areas

• Definable well-orders, Forcing, Large cardinals

ID: 31262368

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