| Abstrakt: |
A hemi-implicative semilattice is an algebra (A , ∧ , → , 1) of type (2, 2, 0) such that (A , ∧ , 1) is a bounded semilattice and the following conditions are satisfied: for every a , b , c ∈ A , if a ≤ b → c then a ∧ b ≤ c and for every a ∈ A , a → a = 1 . The class of hemi-implicative semilattices forms a variety. In this paper we introduce and study a proper subvariety of the variety of hemi-implicative semilattices, ShIS , which also properly contains some varieties of interest for algebraic logic. Our main goal is to show a representation theorem for ShIS . More precisely, we prove that every algebra of ShIS is isomorphic to a subalgebra of a member of ShIS whose underlying bounded semilattice is the bounded semilattice of upsets of a poset. [ABSTRACT FROM AUTHOR] |
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