Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra
Jānis Cīrulis (2012)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Let be a Hilbert algebra. The monoid of all unary operations on generated by operations , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of . This semilattice is isomorphic to the semilattice of finitely generated filters of , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of...