Talk:Subcompact cardinal

Possible error?[edit]

I don't know if this is an error or not: "Existence of subcompact cardinals implies existence of many 1-extendible cardinals, and hence many superstrong cardinals." It appears in the paragraph on quasicompact cardinals, so perhaps "Existence of quasicompact" was intended. The List of large cardinal properties seems to imply that subcompacts are below 1-extendibles in consistency strength. Rsmoore (talk) 06:36, 25 September 2008 (UTC)[reply]

There is no error. The least subcompact cardinal is not 1-extendible (or even measurable), but 1-extendible cardinals are stationary below every subcompact cardinal. The strength of η-extendible cardinals depends on η, and for small η, it is much weaker than extendible. Dmytro (talk) 05:05, 20 August 2018 (UTC)[reply]