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Gödel Part I

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.

Selmer Bringsjord
Wed Apr 24 16:55:41 EDT 1996