McColm conjecture

Yuri Gurevich; Neil Immerman; Saharon Shelah

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McColm conjecture

Yuri Gurevich·Neil Immerman·Saharon Shelah

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Abstract

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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BibTeX RIS

Yuri Gurevich, Neil Immerman, Saharon Shelah. 1994-11-15. McColm conjecture. https://arxiv.org/abs/math/9411235

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