TY - JOUR
T1 - Ramsey theory over partitions II
T2 - Negative Ramsey relations and pump-up theorems
AU - Kojman, Menachem
AU - Rinot, Assaf
AU - Steprāns, Juris
N1 - Publisher Copyright:
© The Hebrew University of Jerusalem 2023.
PY - 2024/6/1
Y1 - 2024/6/1
N2 - In this series of papers we advance Ramsey theory 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 - In this series of papers we advance Ramsey theory 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.
UR - http://www.scopus.com/inward/record.url?scp=85176802430&partnerID=8YFLogxK
U2 - 10.1007/s11856-023-2574-9
DO - 10.1007/s11856-023-2574-9
M3 - Article
AN - SCOPUS:85176802430
SN - 0021-2172
VL - 261
SP - 223
EP - 247
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -