McColm's Conjecture
Yuri G. Gurevich, Neil Immerman, Saharon Shelah · Logic in Computer Science · 1994
Gregory McColm conjectured that positive elementary inductions are bounded in a class K of flnite structures if every (FO + LFP) formula is equivalent to a flrst-order formula in K. Here (FO + LFP) is the extension of flrst-order logic with the least flxed 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.