Epsilon-Logic Is More Expressive Than First-Order Logic Over Finite Structures

There are properties of nite structures that are expressible with the use of Hilbert's-operator in a manner that does not depend on the actual interpretation for-terms, but not expressible in plain rst-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in rst-order logic over nite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power of rst-order logic even as far as de-terministic queries are concerned, thereby answering a question raised by Abiteboul and Vianu.