# Orders of indescribable sets

By Alex Hellsten

2000 *Mathematics Subject Classification*: 03E55, 03C05
*Archive for Mathematical Logic*, 45:705-714, 2006
*Keywords*: Weakly compact cardinal, Weakly compact set,
Saturation of ideal, Mahlo operation

MR2252250, Zbl 1099.03043

We extract some properties of Mahlo's operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.

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