  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.
