Magical Computing

Would it be possible for a wizard to create a universal Turing machine that had an infinite amount of memory?

Also, if we could master magic, do you think that it would be possible to create a separate pocket universe for a computer, that could perform exhaustive searches of an infinite problem space in a way that would seem instant when observed from this universe?

>>18
I = {ø, {ø}, {{ø}}, {{{ø}}}, ...}.  I believe this is just ℕ as Peano numbers, but I might be wrong, I'm rusty on THEORETICAL SHIT THAT DON'T GET SHIT DONE.