  We prove the equivalence of the semantic version of Tarski's theorem on the
undefinability of truth with a semantic version of the Diagonal Lemma, and also
show the equivalence of syntactic Tarski's Undefinability Theorem with a weak
syntactic diagonal lemma. We outline two seemingly diagonal-free proofs for
these theorems from the literature, and show that syntactic Tarski's theorem
can deliver G\"odel-Rosser's Incompleteness Theorem.
