User blog:Wythagoras/Infinite state ITTMs

We define γ[α] = sup (γ[α[1]], γ[α[2]], γ[α[3]], ...) (for some limit ordinal α)

When we get this, the tape history is erased, exepted for those symbols that are written with the state S, and the state is set to S (state limit).

For γ[α+n], we can refer to all n states, and to the first state of the transfinite part.

I'm not sure if it works for λ and ζ.

Values and bounds
We now that sup(γ[1], γ[2], γ[3], ...) = γ itself.

Further, for γ[ω+1] we can take the following ruleset: S _ 1 l ω S 1 1 r halt ω 1 _ r 0 This'll work for γω steps.