The Ixnay function compresses the value expressed in the fast-growing hierarchy into the slow-growing hierarchy within the same ordinals.
It is defined as follows:
Ixnay(j, k) = 0 if j + 1 <= k.
If n >= k: Ixnay(f{α}(n), k) = g{α}(n), where "f" is the fast-growing hierarchy, and "g" is the slow-growing hierarchy.
If n < k: Treat the ordinal level one level lower.
For nested "Ixnay" function, Ixnay^(i+1)(j, k) = Ixnay^i(Ixnay(j, k), k)
Examples:
Ixnay(11, 10) = 0
Ixnay(20, 10) = Ixnay(f{1}(10), 10) = 1
Ixnay(f{3}(2), 10) = Ixnay(f{2}(f{2}(2)), 10) = Ixnay(f{2}(8), 10) = Ixnay(2048, 10) = 1 (because 2,048 < f{2}(10) = 10,240)
Ixnay(f{3}(10), 10) = g{3}(10) = 3
Ixnay(f{10}(10), 10) = Ixnay(f{ω}(10), 10) = g{ω}(10) = 10
Ixnay(G64, 3) = Ixnay(~f{ω+1}(64), 3) = g{ω + 1}(3) = 3 + 1 = 4
Ixnay(G64, 64) = Ixnay(< f{ω+1}(64), 64) = g{ω}(64) = 64
Ixnay(f{ε0}(10), 10) = g{ε0}(10) = 10^^10
Ixnay(f{ψ0(Ω_2)}(10), 10) = g{ψ0(Ω_2)}(10) ~ f{ε0}(10) (using extended Buchholz's function) ~ 10^^8 & 10 in BEAF tetrational arrays