Talk:Bachmann–Howard ordinal
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Merger proposal
editSee here (preferably after reviewing this). --Gro-Tsen (talk) 10:21, 12 April 2008 (UTC)
Can this ordinal be named using the collapsing function?
editThe definition given looks outright wrong. The Bachmann ordinal is the supremum of all ordinals definable using the collapsing function. You can't actually get there using epsilon-sub-omega-plus-one as an argument, that's just a notational convention! Relatively new to Wikipedia so I don't know exactly how to flag this. 76.102.84.197 (talk) 04:45, 22 March 2013 (UTC)
- I believe the definition is correct as given. With the precise definition given at the [ordinal collapsing function] article, ψ(εΩ+1) is the supremum of all values taken by the ψ function (which is constant starting from there). --Gro-Tsen (talk) 17:50, 26 March 2013 (UTC)
Extension of φ
editMentioned here is that this ordinal can be represented using an extension of Veblen's φ, and I believe Bachmann's 1950 φ-functions do this. Here (p.13) is a source, however it's not mentioned if $\varphi^{\mathfrak B}_{\varepsilon_{\Omega+1}}(0)$ is equal to the Bachmann-Howard ordinal. Given that another characterization of this ordinal appears on page 25 using different functions $\psi_{\Omega_n}$, can anyone confirm? If so, this source can be added C7XWiki (talk) 17:34, 13 July 2021 (UTC)