Now, replace our alphabet with
and identify natural numbers with their correlates in binary notation.
To each expression we assign the Gödel number of the expression. We do this according to the following scheme:
The mirror of an expression 
is the expression followed
by its Gödel number.
A sentence is an
expression having one of the following four forms (where 
is any
number): 
, 
, 
, 
.
Naturally, is true iff is the Gödel number of a
printable expression, is true iff is the Gödel number
of an expression whose mirror is printable, and so on.