Omega^omega: Difference between revisions

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* The least limit of additive principal ordinals.
* The least ordinal which is, for all \( n < \omega \), an element of the class \( L^n(\mathrm{Ord}) \), where \( L \) is the limit point operator.
* The proof-theoretic ordinal of second[[Second-order arithmetic with comprehension restricted to |\( \Delta^0_0 mathrm{RCA}_0\)-formulae.]]
* The proof-theoretic ordinal of second[[Second-order arithmetic with comprehension restricted to |\( \Delta^0_0 mathrm{WKL}_0\)-formulae, with Weak König's Lemma adjoined]].
* The proof-theoretic ordinal of Peano arithmetic, with induction restricted to \( \Sigma^0_1 \)-formulae.
* The proof-theoretic ordinal of primitive recursive arithmetic.
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