Free pseudocomplemented semilattices: a new approach. (Q745713)

The concept of a plain pseudocomplemented semilattice is introduced. It is shown that every plain pseudocomplemented semilattice \(S\) is sectionally pseudocomplemented and the canonical form for elements from \(S\) is derived. It is proved that every free pseudocomplemented semilattice is plain. A necessary and sufficient condition for a pseudocomplemented semilattice to be freely generated by a set \(X\) is presented (the main result). If \(F\) is a free pseudocomplemented semilattice then \(B(F)\) is a free Boolean algebra.