Journal of Symbolic Logic

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

Martin Otto

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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.

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J. Symbolic Logic, Volume 65, Issue 4 (2000), 1749-1757.

First available in Project Euclid: 6 July 2007

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Otto, Martin. Epsilon-Logic Is More Expressive Than First-Order Logic over Finite Structures. J. Symbolic Logic 65 (2000), no. 4, 1749--1757.

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