Other Buchholz-like notations
How similar is this to earlier notations based on Hardy hierarchy with respect to fundamental sequences of variants of Buchholz's ordinal notation, such as I-notation? C7X (talk) 04:21, 5 April 2021 (UTC)
- I think that you misread the definition, as the rule 4 is completely different from Buchholz-like expansion. Since Denis has not clarified the set of valid expressions and a proof why it reaches TFBO, I am not certain about whether it actually reaches TFBO. The issue of the lack of the precise definition of the domain is serious, because there seems to be no rule applicable to 10|(((()_1)_2)_1). Therefore to be honest, I doubt that it reaches TFBO.
- p-adic 05:41, 5 April 2021 (UTC)
- It reaches Buchholz's ordinal ψ_0(ψ_ω(0)) using FGH and Buchholz function. I confused ψ_0(ψ_ω(0)) with Takeuti-Feferman-Buchholz ordinal. I fixed this mistake in my blogpost a long time ago, but didn’t do it for the page on my site. For calculation of 10|(((()1)2)1) you can use Online calculator which works using those four rules which are in the definition. It gives 10|(((((((((((((((((((((((((((((((((()0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0)2)1)0 using rule 4.
- Denis Maksudov (talk) 23:02, 5 May 2021 (UTC)
- 1) Some analysis of notation strength is shown in blogpost
- 2) Normal form was not specified but when I created this notation 4 years ago I considered its NF similarly with NF of Buchholz function i.e. if some expression e of Buchholz ordinal notation is written in NF then you can rewrite it as an expression of I-notation using function, which is defined as follows:
- V(0)=empty
- V(D_a(x)+ D_b(y)+ … +D_c(z))= (V(x))_a (V(y))_b … (V(z))_c
- and in this case obtained expression e'=V(e) of I-notation is in NF.
- Denis Maksudov (talk) 00:44, 6 May 2021 (UTC)