Omega^2: Difference between revisions
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The ordinal \( \omega^2 \) is the least ordinal which is a limit of limit ordinals. It is also the growth rate of |
The ordinal \( \omega^2 \) is the least ordinal which is a limit of limit ordinals, as well as the second infinite additive principal ordinal. It is also equal to the proof-theoretic ordinal of rudimentary function arithmetic, and of Peano arithmetic with induction restricted to \( \Delta^0_0 \)-formulae. It is also the approximate growth rate of Conway's chained arrows in the fast-growing hierarchy. |
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Revision as of 13:40, 30 August 2023
The ordinal \( \omega^2 \) is the least ordinal which is a limit of limit ordinals, as well as the second infinite additive principal ordinal. It is also equal to the proof-theoretic ordinal of rudimentary function arithmetic, and of Peano arithmetic with induction restricted to \( \Delta^0_0 \)-formulae. It is also the approximate growth rate of Conway's chained arrows in the fast-growing hierarchy.