TY - JOUR
T1 - Monocolored topological complete graphs in colorings of uncountable complete graphs
AU - Komjáth, P.
AU - Shelah, S.
N1 - Publisher Copyright:
© 2021, Akadémiai Kiadó, Budapest, Hungary.
PY - 2021/2
Y1 - 2021/2
N2 - If κ> ℵ then κ→(κ,TopKκ)2, i.e., every graph on κ vertices contains either an independent set of κ vertices, or a topological Kκ, iff κ is regular and there is no κ-Suslin tree. Concerning the statement ω2→(TopKω2)ω2, i.e., in every coloring of the edges of Kω2 with countably many colors, there is a monochromatic topological Kω2, both the statement and its negation are consistent with the Generalized Continuum Hypothesis.
AB - If κ> ℵ then κ→(κ,TopKκ)2, i.e., every graph on κ vertices contains either an independent set of κ vertices, or a topological Kκ, iff κ is regular and there is no κ-Suslin tree. Concerning the statement ω2→(TopKω2)ω2, i.e., in every coloring of the edges of Kω2 with countably many colors, there is a monochromatic topological Kω2, both the statement and its negation are consistent with the Generalized Continuum Hypothesis.
KW - Suslin tree
KW - forcing
KW - partition relation
UR - http://www.scopus.com/inward/record.url?scp=85100571001&partnerID=8YFLogxK
U2 - 10.1007/s10474-020-01125-3
DO - 10.1007/s10474-020-01125-3
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AN - SCOPUS:85100571001
SN - 0236-5294
VL - 163
SP - 71
EP - 84
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
IS - 1
ER -