Reconstruction of Binary Relations from their Restrictions of Cardinality 2, 3, 4 and (n - 1) I

We prove that any binary relation with underlying set (base) E with cardinality n > 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 arc isomorphic for every subset X of E with cardinality 2, 3,4. In part I1 we shall prove that R and R' arc isomorphic as soon as n > 6 when R / X and R/X' arc isomorphic for every subset X of E with cardinality 2. 3, 4 and ( n 1). 1991 MSC: 04A05