An extension is a mapping from an incompletely ordered set to a completely ordered set.
for "=>" a preorder "=>'" extends "=>" if forall x,y in X x"=>"y => x"=>'"y
example:
X={x,y,z} with x>y,x>z has extensions: y>z, z a strict partial order on a set X => there exists a strict order >'
which extends >