let us say that you have a 600:600 transformer with 40 Henries of primary inductance at 20 Hz,

look at inductive reactance, XL.

at 20 Hz we have 6.28 x 20 Hz x 40 H = 5024 Ohms of Inductive Reactance - XL

does the core have any permeabillity at 20 K? probably not much, maybe 100 mH at best, so

at 20 K Hz we have 6.28 x 20 K Hz x 0.1 Henry = 12,560 Ohms of XL

so even with the core operating at 0.1/40 = 0.0025 of it's original perm, we still have over twice the Reactance,

at 100 K we could use the Permeabillity of air to get enough Reactance? let's see,

5,000 Ohms = 6.28 x 100,000 x Henries, H = 8 milli-Henries,

pick a 50 EI core and figure perm,

for 50 EI, L=0.2657 x 10^-8 x K1 Stacking x N^2 x U-ac

so 0.008 Henries = 0.2657^-8 x 0.9 x 600 Turns ^ 2 x U-ac

U-ac = 0.008 / 0.000861 = 9

relative perm = U/U-o with U-o = 1 exactly, so we only need a core with 9 times the perm of air at 100 K with a 600 ohm primary, copper has enough impurities to supply enough perm to keep the transformer running by itself with no core,

you can try this, look at in/out with a dual trace scope at 100 K Hz and remove the core,