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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