This program analyzes Buchholz ψ function defined in Buchholz (1986). When the user gives an ordinal term a ∈ T, as defined in the reference, the program determines if a ∈ OT. If a ∉ OT, b ∈ OT (o(a) = o(b)) is suggested. For example:
Input: D1(D0(0),D1(D4(0)),D3(D0(0))) a = D1(D0(0),D1(D4(0)),D3(D0(0))) where a ∈ T, a ∉ OT. Showing b ∈ OT where o(a) = o(b): b = D1(D3(D0(0)),D2(0)) o(a) = o(b) = ψ1(ψ3(ψ0(0))+ψ2(0)) = ψ1(ψ3(1)+ψ2(0))
Examples
Rules
Buchholz, W. (1986): A New System of Proof-Theoretic Ordinal Function. Annals of Pure and Applied Logic, 32:195-207.
Buchholz ψ analyzer 1.0 by Fish