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

Preview

PDF (lf_submitted) - Draft Version Download (1MB) | Preview

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.

Item Type:	Article
Uncontrolled Keywords:	definable well-orders,forcing,large cardinals
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Pure Connector
Date Deposited:	09 Jul 2014 12:06
Last Modified:	07 Nov 2024 12:37
URI:	https://ueaeprints.uea.ac.uk/id/eprint/49077
DOI:	10.1016/j.apal.2014.11.010

Downloads

Actions (login required)

View Item