RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (<i>n</i> ‐ 1) I

Abstract

Abstract We prove that any binary relation with underlying set (base) E with cardinality n &gt; 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and ( n ‐ 1). In part I we characterize relations R and R ' on the same base E such that R/X and R'/X are isomorphic for every subset X of E with cardinality 2, 3, 4. In part II we shall prove that R and R ' are isomorphic as soon as n &gt; 6 when R/X and R/X ' are isomorphic for every subset X of E with cardinality 2, 3, 4 and ( n ‐ 1).