Epsilon-Logic is More Expressive than First-Order Logic over Finite Structures

There are properties of finite structures that are expressible with the use of Hilbert's epsilon -operator in a manner that does not depend on the actual interpretation for epsilon -terms. but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich. concerning the invariant use of an auxiliary ordering in first-order logic over finite 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 first-order logic even as far as deterministic queries are concerned. thereby answering a question raised by Abiteboul and Vianu.