Diagonalization Lemma
In
mathematical logic
, the
diagonalization lemma
states that for any
well formed formula
\phi(x)
with a
free variable
x
, there is a sentence ψ such that
P \vdash \psi\leftrightarrow\phi(
\psi
)
where
ψ
is the Gödel number for ψ.
Gödel's first incompleteness theorem
can be proved via the diagonalization lemma. It takes its name from
Cantor's diagonal argument
to prove that the
real numbers
are uncountable.
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