Definability of Arithmetic Operations from the Order and a Random Relation1
Ivan Korec · Fundamenta Informaticae · 1993
For almost all binary relations R ⊆ N 2 the addition and multiplication on the set N of nonnegative integers (and hence all arithmetical relations) are first order definable in the structure (N; ⩽, R). The defining formulae can be chosen independently on R and the words “for almost all” mean “with probability 1” by a very natural probability measure.