Let be the ring of all entire functions of one complex variable, and let DA be the subring of those entire functions that are differentially algebraic (DA); that is, they satisfy a nontrivial algebraic differential equation.

where P is a non-identically-zero polynomial in its n + 2 variables. It seems not to be known whether DA is elementarily equivalent to . This would mean that DA and have exactly the same true statements about them, in the first-order language of rings. (Roughly speaking, a sentence about a ring R is first-order if it has finite length and quantifies only over elements (i.e., not subsets or functions or relations) of R.) It follows from [NAN] that DA and are not isomorphic as rings, but this does not answer the question of elementary equivalence.