According to Gödel’s incompleteness theorems,  the statement that Peano Arithmetic (PA) is consistent, in its guise as a number-theoretic statement (given the technique of Gödel numbering), cannot be derived in PA itself. But PA can be strengthened by adding this consistency statement or by stronger axioms. In particular, axioms partially expressing the soundness of PA can be added. These are known as reflection principles. An example of a reflection principle for PA would be the set of sentences \(Bew_{PA}(\ulcorner \phi \urcorner) \rightarrow \phi\) where \(\phi\) is a formula of the language of arithmetic, \(\ulcorner \phi \urcorner\) a name for \(\phi\) and \(Bew_{PA}(x)\) is the standard provability predicate for PA (‘\(Bew\)’ was introduced by Gödel and is short for the German word ‘beweisbar’, that is, ‘provable’). 