Bad

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An ordinal is called bad if the supremum of order types of $\alpha$-recursive well-orderings is less than the next admissible after $\alpha$. Since the least bad ordinal is quite large (larger than the least $\Pi_1^1$-reflecting ordinal [1]), this behavior appears unexpectedly when working with ordinals in the range of weakened versions of stability. [2]

Relation to other conditions