Abstract. An asymptotic result in finite combinatorics is stated in terms of a sufficiently large finite object. In set theory it seemed that the only absolute equations that hold for all sufficiently large cardinals are X^n=X, which hold for all infinite cardinals X and finite n>0. We discuss other equations which hold without additional axioms for an infinite cardinal \nu instead of n for all sufficiently large X. These equations lead to a weak infinitary Löwenheim-Skolem theorem, which in turn gives several combinatorial theorem in ZFC which will be ! sketched in the talk and at least one of which will be proved in full.