Symbolic Logic; April 25

Selmer Bringsjord

Gödel numbering scheme

** The Diagonalization of a Formula**

Let **A** be an expression having gödel number **n**. Then define
to be the expression ** n**. The ** diagonalization**
of **A** is the expression

Then if **A** is a formula in **L**, the language of arithmetic, that contains
just the variable **x** free, the diagonalization of **A** will be a sentence
that ``says that" **A** is true of its own gödel number.

** Lemma I**

There is a recursive function, diag, which works like this.
If **n** is the gödel number of an expression **A**, diag(**n**) is the
gödel number of the diagonalization of **A**.

Wed Apr 24 16:55:41 EDT 1996