User blog comment:Ubersketch/A proposal for a standard/@comment-35470197-20190811012241/@comment-35470197-20190813013819

@Ubersketch

Please write down the whole algorithm to determine x < y without any oracle. Or don't you understand that "checking unbounded ∃ sentence" does not give an algorithm without oracle? Or don't you understand that in your definition of FS, you actually used ∈-relation for possibly uncountably many ordinals? Or do youn't you understand that "there is a rule applicable to any case" does not imply the termination of the computation? Or don't you understand that well-defined recursion in set theory does not necessarily give an alogorithm? Or should I ask you to compute ψ_{Ω_1}(χ_{χ_0(ψ_{χ_K(0,0)}(χ_{χ_0(1,1)}(0,0))}(0,1))[7] in the notation which you referred in order to tell you that you have no algorithm?