| Abstract |
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A first-order sentence \theta of vocabulary \sigma \cup {S} is successor-invariant in the finite if for every finite \sigma-structure M and successor relations S1 and S2 on M, (M,S1) \models \theta \iff (M, S2) \models \theta. In this paper I give an example of a non-first-order definable class of finite structures which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for order-invariance in the finite, due to Y. Gurevich.
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 Additional Information
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Citation:
Benjamin Rossman,
"Successor-Invariance in the Finite,"
lics,
p. 148,
18th Annual IEEE Symposium on Logic in Computer Science (LICS'03),
2003
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