 It thus follows that \(\textrm{TA}\) is \(\Delta^1_1\)-definable. On the other hand, it follows from Tarski’s Theorem on the undefinability of truth that \(\textrm{TA}\) is not arithmetically definable— i.e. \(\textrm{TA} \not\in \Sigma^0_n \cup \Pi^0_n\) for any \(n \in \mathbb{N}\). This in turn shows that the analytical sets properly extend the arithmetical ones.