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Epsilon-logic is more expressive than first-order logic over finite structures

Published online by Cambridge University Press:  12 March 2014

Martin Otto
Martin Otto*
Affiliation:
Department of Computer Science, University of Wales, Swansea, Swansea SA2 8PP, UK, E-mail:m.otto@swan.ac.uk
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Abstract

There are properties of finite 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 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1749 - 1757
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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