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Namely, it gives a uniform approach to geometries defined by various fragments of the initial language. The next prospective application deals with effective recognition of sets and effective computations with properties that can be defined by formulas from a fragment of the original language. In this way, one can get an effective syntactical expression by semantic tools. Yet another advantage is a common approach to generalizations of the main model theoretic concepts to the sublanguages of the first-order language and revealing new connections between well-known concepts. The fourth application concerns the generalization of the unification theory, or more generally Term Rewriting Theory, to the logic unification theory.<\/jats:p>","DOI":"10.1142\/s0218196718400106","type":"journal-article","created":{"date-parts":[[2018,8,3]],"date-time":"2018-08-03T09:36:21Z","timestamp":1533288981000},"page":"1585-1612","source":"Crossref","is-referenced-by-count":1,"title":["Action of endomorphism semigroups on definable sets"],"prefix":"10.1142","volume":"28","author":[{"given":"G.","family":"Mashevitzky","sequence":"first","affiliation":[{"name":"Ben Gurion University of the Negev, Beersheba, Israel"}]},{"given":"B.","family":"Plotkin","sequence":"additional","affiliation":[{"name":"Hebrew University, Jerusalem, Israel"}]},{"given":"E.","family":"Plotkin","sequence":"additional","affiliation":[{"name":"Bar Ilan University, Ramat Gan 5290002, Israel"}]}],"member":"219","published-online":{"date-parts":[[2019,1,14]]},"reference":[{"key":"S0218196718400106BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-63246-8_2"},{"key":"S0218196718400106BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172752"},{"key":"S0218196718400106BIB003","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/oso\/9780198537465.003.0002","volume-title":"Handbook of Logic in Artificial Intelligence and Logic Programming","volume":"2","author":"Baader F.","year":"1994"},{"key":"S0218196718400106BIB004","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609303002480"},{"key":"S0218196718400106BIB006","doi-asserted-by":"publisher","DOI":"10.2168\/LMCS-3(1:2)2007"},{"key":"S0218196718400106BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-007-2026-0"},{"key":"S0218196718400106BIB008","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exi083"},{"key":"S0218196718400106BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-011-0110-y"},{"key":"S0218196718400106BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01070906"},{"key":"S0218196718400106BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/12413"},{"key":"S0218196718400106BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3466-1_12"},{"key":"S0218196718400106BIB014","first-page":"xii+550","volume-title":"Studies in Logic and the Foundations of Mathematics","volume":"73","author":"Chang C. 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