## On supercompactness and the continuum function

- Brent Cody, Menachem Magidor
- Ann. Pure Appl. Logic
- 2014

@article{Cody2012TheFO, title={The failure of GCH at a degree of supercompactness}, author={Brent Cody}, journal={Math. Log. Q.}, year={2012}, volume={58}, pages={83-94} }

- Published 2012 in Math. Log. Q.
DOI:10.1002/malq.201020078

We determine the large cardinal consistency strength of the existence of a λ-supercompact cardinal κ such that GCH fails at λ. Indeed, we show that the existence of a λ-supercompact cardinal κ such that 2 ≥ θ is equiconsistent with the existence of a λ-supercompact cardinal that is also θ-tall. We also prove some basic facts about the large cardinal notion of tallness with closure.