{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:35:01Z","timestamp":1777646101580,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[1998,1,1]],"date-time":"1998-01-01T00:00:00Z","timestamp":883612800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>The notion of Scott consequence system (briefly, S-system) was introduced by D. Vakarelov in [32] in an analogy to a similar notion given by D. Scott in [26]. 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. Vakarelov [32] 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.<\/jats:p>","DOI":"10.3233\/fi-1998-33103","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T21:22:31Z","timestamp":1575321751000},"page":"43-70","source":"Crossref","is-referenced-by-count":5,"title":["On Scott Consequence Systems"],"prefix":"10.1177","volume":"33","author":[{"given":"Georgi","family":"Dimov","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Sofia, Blvd. J.Bouchier 5, 1126 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dimiter","family":"Vakarelov","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Sofia, Blvd. J.Bouchier 5, 1126 Sofia, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1998,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-1998-33103","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-1998-33103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:34:19Z","timestamp":1777444459000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-1998-33103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.3233\/FI-1998-33103"],"URL":"https:\/\/doi.org\/10.3233\/fi-1998-33103","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}