Frames and MV-algebras

Studia Logica 81 (3):357 - 385 (2005)
We describe a class of MV-algebras which is a natural generalization of the class of “algebras of continuous functions”. More specifically, we're interested in the algebra of frame maps Hom (Ω(A), K) in the category T of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame. Given a topological space X and a topological MV-algebra A, we have the algebra C (X, A) of continuous functions from X to A. We can look at this from a frame point of view. Among others we have the result: if K is spatial, then C(pt(K), A), pt(K) the points of K, embeds into Hom (Ω(A), K) analogous to the case of C (X, A) embedding into Hom (Ω(A), Ω (X))
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1007/s11225-005-4649-5
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