We study ineffability, the Shelah property, and indescribability of when . We prove that if is a strong limit cardinal with then the ineffable ideal, the Shelah ideal, and the completely ineffable ideal over are the same, and that it can be precipitous. Furthermore we show that -indescribability of is much stronger than ineffability if .
Toshimichi USUBA. "Ineffability of for with small cofinality." J. Math. Soc. Japan 60 (3) 935 - 954, July, 2008. https://doi.org/10.2969/jmsj/06030935