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Quasi-implication algebras

Ivan Chajda, Kamil Dušek (2002)

Discussiones Mathematicae - General Algebra and Applications

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.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

The paper continues the investigation of quasitrivial semimodules and related problems. In particular, endomorphisms of semilattices are investigated.

Quasitrivial semimodules. VII.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

The paper continues the investigation of quasitrivial semimodules and related problems. In particular, strong endomorphisms of semilattices are studied.

Quasivarieties of pseudocomplemented semilattices

M. Adams, Wiesław Dziobiak, Matthew Gould, Jürg Schmid (1995)

Fundamenta Mathematicae

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 2 ω quasivarieties.

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