Geodesic
Maximum predicate descriptions of sets of mappings
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1636-1648

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The work is carried out in the framework of the algebraic approach and is devoted to the problem of describing sets of mappings by pairs of m-place predicates. Maximum descriptions are distinguished in the set of all predicate descriptions, and necessary and sufficient maximality conditions are obtained. Using a partial order and betweenness relations as examples, it is shown that, for a given predicate on the set of values, the necessary maximality conditions imply some properties of this predicate on its domain. Taking this fact into account, a set of axioms for the betweenness relation is proposed, and examples of such relations are considered. 
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     author = {R. S. Takhanov},
     title = {Maximum predicate descriptions of sets of mappings},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1636--1648},
     publisher = {mathdoc},
     volume = {47},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a16/}
}
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R. S. Takhanov. Maximum predicate descriptions of sets of mappings. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1636-1648. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a16/