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?

>>13
There exists a set I such that the following properties are true:
! ø ∈ I
! for all x ∈ I: (x ∪ {x}) ∈ I