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Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra

Jānis Cīrulis (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let A : = ( A , , 1 ) be a Hilbert algebra. The monoid of all unary operations on A generated by operations α p : x ( p x ) , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of A . This semilattice is isomorphic to the semilattice of finitely generated filters of A , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of A . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of A , and the...

Bourbaki's Fixpoint Lemma reconsidered

Bernhard Banaschewski (1992)

Commentationes Mathematicae Universitatis Carolinae

A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L . This is then used to deal with coproducts and other aspects of frames.

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