TY - UNPB
T1 - Ramsey theory over partitions II
T2 - Negative Ramsey relations and pump-up theorems
AU - Kojman, Menachem
AU - Rinot, Assaf
AU - Steprans, Juris
N1 - A sequel to arXiv:2102.07241
PY - 2022/4/16
Y1 - 2022/4/16
N2 - Abstract. In this series of papers we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21]. It is shown that for every infinite cardinal λ, a strong coloring on λ + by λ colors over a partition can be stretched to one with λ + colors over the same partition. Also, a sufficient condition is given for when a strong coloring witnessing Pr1(. . .) over a partition may be improved to witness Pr0(. . .). Since the classical theory corresponds to the special case of a partition with just one cell, the two results generalize pump-up theorems due to Eisworth and Shelah, respectively.
AB - Abstract. In this series of papers we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21]. It is shown that for every infinite cardinal λ, a strong coloring on λ + by λ colors over a partition can be stretched to one with λ + colors over the same partition. Also, a sufficient condition is given for when a strong coloring witnessing Pr1(. . .) over a partition may be improved to witness Pr0(. . .). Since the classical theory corresponds to the special case of a partition with just one cell, the two results generalize pump-up theorems due to Eisworth and Shelah, respectively.
KW - math.LO
KW - 03E02
U2 - 10.48550/arXiv.2204.14101
DO - 10.48550/arXiv.2204.14101
M3 - Preprint
BT - Ramsey theory over partitions II
ER -