Forcing lightface definable well-orders without the CGH

Aspero, David, Holy, Peter and Luecke, Philipp (2015) Forcing lightface definable well-orders without the CGH. Annals of Pure and Applied Logic, 166 (5). 553–582. ISSN 0168-0072

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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.

Item Type: Article
Uncontrolled Keywords: definable well-orders,forcing,large cardinals
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
Depositing User: Pure Connector
Date Deposited: 09 Jul 2014 12:06
Last Modified: 24 Oct 2022 06:30
DOI: 10.1016/j.apal.2014.11.010


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