### McColm Conjecture

by Gurevich and Immerman and Shelah. [GISh:525]

Symposium on Logic in Computer Science, 1994

Gregory McColm conjectured that positive elementary
inductions are bounded in a class K of finite structures if
every (FO + LFP) formula is equivalent to a first-order
formula in K . Here (FO + LFP) is the extension of
first-order logic with the least fixed point operator. We
disprove the conjecture. Our main results are two
model-theoretic constructions, one deterministic and the other
randomized, each of which refutes McColm's conjecture.

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