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Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers |
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| Authors: | Menachem Kojman Gyesik Lee Eran Omri Andreas Weiermann |
| Affiliation: | aDepartment of Mathematics, Ben Gurion University of the Negev, PO Box 653, Be'er Sheva, Israel;bLIX, INRIA Futurs, Ecole Polytechnique, 91128 Palaiseau Cedex, France;cDepartment of Computer Science, Ben Gurion University of the Negev, PO Box 653, Be'er Sheva, Israel;dVakgroep Zuivere Wiskunde en Computeralgebra, Ghent University, Krijgslaan 281, Gebouw S22 B9000, Gent, Belgium |
| 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: | Paris– Harrington theorem Kanamori– McAloon theorem Ackermannian functions Rapidly growing Ramsey numbers |
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