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The Bachmann-Howard ordinal is a large ordinal, significant for being the proof-theoretic ordinal of Kripke-Platek set theory with the axiom of infinity. It is the supremum of \(\vartheta(\alpha)\) (using Weiermann's \(\vartheta\)) for all \(\alpha < \varepsilon_{\Omega+1}\). An early version of Bird's array notation was limited by \(\vartheta(\varepsilon_{\Omega+1})\).

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  • Bachmann-Howard ordinal
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  • The Bachmann-Howard ordinal is a large ordinal, significant for being the proof-theoretic ordinal of Kripke-Platek set theory with the axiom of infinity. It is the supremum of \(\vartheta(\alpha)\) (using Weiermann's \(\vartheta\)) for all \(\alpha < \varepsilon_{\Omega+1}\). An early version of Bird's array notation was limited by \(\vartheta(\varepsilon_{\Omega+1})\).
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abstract
  • The Bachmann-Howard ordinal is a large ordinal, significant for being the proof-theoretic ordinal of Kripke-Platek set theory with the axiom of infinity. It is the supremum of \(\vartheta(\alpha)\) (using Weiermann's \(\vartheta\)) for all \(\alpha < \varepsilon_{\Omega+1}\). An early version of Bird's array notation was limited by \(\vartheta(\varepsilon_{\Omega+1})\).
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