# Measurable cardinals and good -wellorderings

@article{Lcke2018MeasurableCA,
title={Measurable cardinals and good -wellorderings},
author={Philipp L{\"u}cke and Philipp Schlicht},
journal={Math. Log. Q.},
year={2018},
volume={64},
pages={207-217}
}
• Published 1 July 2018
• Computer Science
• Math. Log. Q.
We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals κ with the property that the collection of all initial segments of the wellordering is definable by a Σ1-formula with parameter κ. A short argument shows that the existence of a measurable cardinal δ implies that such wellorderings do not exist at δ-inaccessible cardinals of cofinality not equal to δ and their successors. In contrast, our main result shows that these…
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