Epsilon-logic is more expressive than first-order logic over finite structures
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AbstractThere 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.
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2002 ◽
Vol 8
(3)
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pp. 380-403
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1999 ◽
Vol Vol. 3 no. 3
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2005 ◽
Vol 70
(3)
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pp. 696-712
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2009 ◽
Vol 74
(1)
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pp. 168-186
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