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?

>>21
The definition I gave (standard construction) produces:

I = {ø, {ø}, {ø, {ø}}, {ø, {ø}, {ø, {ø}}}, ...}

You could also do for all x ∈ I: {x} ∈ I, which is what you gave. Generally you just need a successor function S then for each element e in the set, S(e) is also in the set.