TY - JOUR
T1 - Complicated colorings, revisited
AU - Rinot, Assaf
AU - Zhang, Jing
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/4
Y1 - 2023/4
N2 - In a paper from 1997, Shelah asked whether Pr1(λ+,λ+,λ+,λ) holds for every inaccessible cardinal λ. Here, we prove that an affirmative answer follows from □(λ+). Furthermore, we establish that for every pair χ<κ of regular uncountable cardinals, □(κ) implies Pr1(κ,κ,κ,χ).
AB - In a paper from 1997, Shelah asked whether Pr1(λ+,λ+,λ+,λ) holds for every inaccessible cardinal λ. Here, we prove that an affirmative answer follows from □(λ+). Furthermore, we establish that for every pair χ<κ of regular uncountable cardinals, □(κ) implies Pr1(κ,κ,κ,χ).
KW - Square
KW - Strong colorings
KW - Walks on ordinals
UR - http://www.scopus.com/inward/record.url?scp=85147364561&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2022.103243
DO - 10.1016/j.apal.2022.103243
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AN - SCOPUS:85147364561
SN - 0168-0072
VL - 174
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 4
M1 - 103243
ER -