Minimally incomplete sets of Łukasiewiczian truth functions (Q796515)

An n-valued truth function is called pure if it is closed on the set \(\{1,n\}\). And, if it can be defined by composition from \(\neg\) and \(\to\), it is said to be Łukasiewiczian or an Ł\(_ n-function\). The author shows the following equivalences for \(n>2:\) a) n-1 is prime; b) the set of Ł\(_ n-functions\) coincides with the set of pure n-valued functions; c) \(\{ \neg,\to,f\}\) is functionally complete if f is non- Łukasiewiczian.