RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (n ‐ 1) I
Gérard Lopez, Claire Rauzy · Mathematical logic quarterly · 1992
Abstract 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 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 > 6 when R/X and R/X' are isomorphic for every subset X of E with cardinality 2, 3, 4 and (n ‐ 1).