Quasicomplemented semilattices
Quasi-implication algebras
A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having non-involutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence between this algebra and a quasi-implication algebra is shown.
Quasitrivial semimodules. VI.
The paper continues the investigation of quasitrivial semimodules and related problems. In particular, endomorphisms of semilattices are investigated.
Quasitrivial semimodules. VII.
The paper continues the investigation of quasitrivial semimodules and related problems. In particular, strong endomorphisms of semilattices are studied.
Quasivarieties of pseudocomplemented semilattices
Two properties of the lattice of quasivarieties of pseudocomplemented semilattices are established, namely, in the quasivariety generated by the 3-element chain, there is a sublattice freely generated by ω elements and there are quasivarieties.