Boolean equations and Post classes (Q1409080)

The important achievement in the classification of the set of Boolean functions \(C_1\) was the construction by \textit{E. Post} [The two-valued iterative systems of mathematical logic. Princeton, NJ: Princeton Univ. Press (1941; Zbl 0063.06326)] of the complete list of all closed classes. It was particularly shown that the Boolean function set is countable and it can be described either by direct enumeration of functions or by indicating the characteristic property or a combination of properties which allow to determine easily to which of the classes a function from \(C_1\) belongs. In the present article Boolean equations describing the corresponding series of the closed Post classes are found.