Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers

Menachem Kojman; Gyesik Lee; Eran Omri; Andreas Weiermann

doi:10.1016/j.jcta.2007.12.006

Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers

Menachem Kojman
, Gyesik Lee
, Eran Omri
, Andreas Weiermann

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We compute the sharp thresholds on g at which g-large and g-regressive Ramsey numbers cease to be primitive recursive and become Ackermannian. We also identify the threshold below which g-regressive colorings have usual Ramsey numbers, that is, admit homogeneous, rather than just min-homogeneous sets.

Original language	English
Pages (from-to)	1036-1055
Number of pages	20
Journal	Journal of Combinatorial Theory. Series A
Volume	115
Issue number	6
DOIs	https://doi.org/10.1016/j.jcta.2007.12.006
State	Published - Aug 2008
Externally published	Yes

Keywords

Ackermannian functions
Kanamori-McAloon theorem
Paris-Harrington theorem
Rapidly growing Ramsey numbers

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10.1016/j.jcta.2007.12.006

Cite this

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title = "Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers",

abstract = "We compute the sharp thresholds on g at which g-large and g-regressive Ramsey numbers cease to be primitive recursive and become Ackermannian. We also identify the threshold below which g-regressive colorings have usual Ramsey numbers, that is, admit homogeneous, rather than just min-homogeneous sets.",

keywords = "Ackermannian functions, Kanamori-McAloon theorem, Paris-Harrington theorem, Rapidly growing Ramsey numbers",

author = "Menachem Kojman and Gyesik Lee and Eran Omri and Andreas Weiermann",

note = "Funding Information: E-mail addresses: [email protected] (M. Kojman), [email protected] (G. Lee), [email protected] (E. Omri), [email protected] (A. Weiermann). 1 Supported by a German–Israeli Foundation for Scientific Research and Development grant I-802-195.6. 2 Supported by DFG grant WE 2178/4-1 during PhD at University of M{\"u}nster, Germany.",

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doi = "10.1016/j.jcta.2007.12.006",

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journal = "Journal of Combinatorial Theory. Series A",

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AU - Kojman, Menachem

AU - Lee, Gyesik

AU - Omri, Eran

AU - Weiermann, Andreas

N1 - Funding Information: E-mail addresses: [email protected] (M. Kojman), [email protected] (G. Lee), [email protected] (E. Omri), [email protected] (A. Weiermann). 1 Supported by a German–Israeli Foundation for Scientific Research and Development grant I-802-195.6. 2 Supported by DFG grant WE 2178/4-1 during PhD at University of Münster, Germany.

PY - 2008/8

Y1 - 2008/8

N2 - We compute the sharp thresholds on g at which g-large and g-regressive Ramsey numbers cease to be primitive recursive and become Ackermannian. We also identify the threshold below which g-regressive colorings have usual Ramsey numbers, that is, admit homogeneous, rather than just min-homogeneous sets.

AB - We compute the sharp thresholds on g at which g-large and g-regressive Ramsey numbers cease to be primitive recursive and become Ackermannian. We also identify the threshold below which g-regressive colorings have usual Ramsey numbers, that is, admit homogeneous, rather than just min-homogeneous sets.

KW - Ackermannian functions

KW - Kanamori-McAloon theorem

KW - Paris-Harrington theorem

KW - Rapidly growing Ramsey numbers

UR - https://www.scopus.com/pages/publications/44149092392

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DO - 10.1016/j.jcta.2007.12.006

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SN - 0097-3165

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 6

ER -

Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers

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Keywords

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