Our definiendum will be `x x is a physical computer.' As you can
see, we have no trouble whatever defining non-physical (= mathematical)
machines; indeed, the definition employs 
, now the
infinite list of all machines in the Arithmetic Hierarchy
(the start of the Turing uncomputable portion of AH is easily viewed as
a collection of machines). So, the definition employs both the
type 3 to type 0 Chomsky Hierarchy, and the Arithmetic Hierarchy
For any two machine
types T and 
, we write 
iff T is less or equal in power
to 
.
)
