 Any set of finite sequences of words that can be produced by a normal system is called a normal set. Post was able to show that for any canonical set C over some alphabet \(\Sigma\) there is a normal set N over an alphabet \(\Delta\) with \(\Sigma \subseteq \Delta\) such that \(C = N \cap \Sigma^{\ast}\). It was his conviction that (1) any set of finite sequences that can be generated by finite means can be generated by canonical systems and (2) the proof that for every canonical set there is a normal set which contains it, which resulted in Post’s thesis I: