Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.):
- (9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula representing the relation: y is (Gödel number of) the right-hand side of the biconditional (whose Gödel number is) x. Diagonalization then yields a formula G such that PAs (Paeno arithmetic , 's' stands for standard language)
- (10) G≡[Tr(
G,y)∧¬Tr(y))], where, as usual,
Gabbreviates the numeral denoting the Gödel number of the formula G.
How (10) can be derived from (9) trough Diagonalization?