User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-5029411-20130809210243/@comment-1605058-20130810093626

Interesting note: weakly compact cardinal is Pi11 indescribable. We can define such cardinals abstractly, e.g. let \(\Pi(m,n)\) denote first \(\Pi^m_n\) indescribable cardinal.