TY - JOUR

T1 - A note on edge colorings and trees

AU - Jarden, Adi

AU - Shami, Ziv

N1 - Publisher Copyright:
© 2022 Wiley-VCH GmbH.

PY - 2022/11

Y1 - 2022/11

N2 - We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal κ has a homogeneous set of size κ provided that the number of colors μ satisfies (Formula presented.). Another result is that an uncountable cardinal κ is weakly compact if and only if κ is regular, has the tree property, and for each (Formula presented.) there exists (Formula presented.) such that every tree of height μ with λ nodes has less than (Formula presented.) branches.

AB - We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal κ has a homogeneous set of size κ provided that the number of colors μ satisfies (Formula presented.). Another result is that an uncountable cardinal κ is weakly compact if and only if κ is regular, has the tree property, and for each (Formula presented.) there exists (Formula presented.) such that every tree of height μ with λ nodes has less than (Formula presented.) branches.

UR - http://www.scopus.com/inward/record.url?scp=85136488647&partnerID=8YFLogxK

U2 - 10.1002/malq.202100019

DO - 10.1002/malq.202100019

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AN - SCOPUS:85136488647

SN - 0942-5616

VL - 68

SP - 447

EP - 457

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 4

ER -