On Scott consequence systems

• Autorzy: Dimov G. , Vakarelov D.
• Języki publikacji: EN

Abstrakty

EN

The notion of Scott consequence system (briefly, S-system) was introduced by D.Vakarelov in an analogy to a similar notion given by D. Scott. In part one of the paper we study the category Ssyst of all S-systems and all their morphisms. We show that the category DLat of all distributive lattices and all lattice homomorphisms is isomorphic to a reflective full subcategory of the category Ssyst. Extending the representation theory of D. Vakarelo for S-systems in P-systems, we develop an isomorphism theory for S-systems and for Tarski consequence systems. In part two of the paper we prove that the separation theorem for S-systems is equivalent in ZF to some other separation principles, including the separation theorem for filters and ideals in Boolean algebras and separation theorem for convex sets in convexity spaces.

Słowa kluczowe

EN

Stone space; adjoint functors; axiom of choice

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 1998
• Tom: Vol. 33, nr 1
• Strony: 43--70
• Opis fizyczny: bibliogr. 33 poz.

Twórcy

autor

Dimov G.

autor

Vakarelov D.

• Department of mathematics and Computer Science, University of Sofia Blvd. J. Bouchier 5, 1126 Sofia, Bulgaria,