We wish to make a correction to our paper On definability of ordinals in logic with infinitely long expressions (this journal, vol. 31 (1966), pp. 365–375). Let Ω be an infinite singular cardinal and Ω+ the smallest cardinal >Ω. For the proof of the second half of Theorem 3, we incorrectly assumed that an ordinal γ is not definable in LΩ, if γ is not cofinal with any ordinal ≤Ω. However, Ω+ is indeed definable in LΩ and Theorem 3 should read:
If Ω singular, then an ordinal α is definable in Lα, if and only if σ ≤ exp(Ω+, Ω+), where exp (β,γ) denotes ordinal exponentiation βγ.