McColm conjecture
<|reference_start|>McColm conjecture: 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.<|reference_end|>
@article{gurevich1994mccolm,
    title={McColm conjecture},
    author={Yuri Gurevich, Neil Immerman, Saharon Shelah},
    journal={Symposium on Logic in Computer Science (1994), 10--19},
    year={1994},
    number={Shelah [GISh:525]},
    archivePrefix={arXiv},
    eprint={math/9411235},
    primaryClass={math.LO cs.LO}
}