McColm's conjecture

Yuri Gurevich; Neil Immerman; Saharon Shelah

McColm's conjecture

Yuri Gurevich^*, Neil Immerman, Saharon Shelah

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

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.

Original language	English
Title of host publication	Proceedings - Symposium on Logic in Computer Science
Publisher	Publ by IEEE
Pages	10-19
Number of pages	10
ISBN (Print)	081866312X
State	Published - 1994
Externally published	Yes
Event	Proceedings of the 1994 IEEE 9th Annual Symposium on Logic in Computer Science - Paris, Fr Duration: 4 Jul 1994 → 7 Jul 1994

Publication series

Name	Proceedings - Symposium on Logic in Computer Science

Conference

Conference	Proceedings of the 1994 IEEE 9th Annual Symposium on Logic in Computer Science
City	Paris, Fr
Period	4/07/94 → 7/07/94

Cite this

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title = "McColm's conjecture",

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.",

author = "Yuri Gurevich and Neil Immerman and Saharon Shelah",

year = "1994",

language = "אנגלית",

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series = "Proceedings - Symposium on Logic in Computer Science",

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note = "Proceedings of the 1994 IEEE 9th Annual Symposium on Logic in Computer Science ; Conference date: 04-07-1994 Through 07-07-1994",

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AU - Immerman, Neil

AU - Shelah, Saharon

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AB - 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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PB - Publ by IEEE

T2 - Proceedings of the 1994 IEEE 9th Annual Symposium on Logic in Computer Science

Y2 - 4 July 1994 through 7 July 1994

ER -

McColm's conjecture

Abstract

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