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Abstract: We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes... (Update)
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1.5: Fixed Point vs. First-Order Logic on Finite Ordered.. - Kfoury, Wymann-Böni (1993) (Correct)
0.8: A Characterization of First-Order Definable Subsets on.. - Kfoury, Wymann-Böni (1993) (Correct)
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BibTeX entry: (Update)
@techreport{ kfoury93fixed,
author = "A. J. Kfoury and M. Wymann-B{\"o}ni",
title = "Fixed Point vs. First-Order Logic on Finite Ordered Structures with Unary Relations",
number = "008",
year = "1993",
url = "citeseer.ist.psu.edu/kfoury93fixed.html" }
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2 of Pure and Applied Logic (context) - arithmetic, Ann - 1990
2 Sur quelques classifications des syst`emes de relations (context) - Fraiss'e - 1954
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