McColm conjecture
逻辑
2016-09-06 v1 计算机科学中的逻辑
摘要
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.
引用
@article{arxiv.math/9411235,
title = {McColm conjecture},
author = {Yuri Gurevich and Neil Immerman and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9411235},
year = {2016}
}