Talk:Bachmann–Howard ordinal
 | This article is rated Stub-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
Merger proposal[edit]
See here (preferably after reviewing this). --Gro-Tsen (talk) 10:21, 12 April 2008 (UTC)
Can this ordinal be named using the collapsing function?[edit]
The 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[edit]
Mentioned 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)