TY - JOUR
T1 - Coloring finite subsets of uncountable sets
AU - Komjáth, Péter
AU - Shelah, Saharon
PY - 1996
Y1 - 1996
N2 - It is consistent for every 1 ≤ n < ω that 2ω = ωn and there is a function F : [ωn]<ω → ω such that every finite set can be written in at most 2n-1 ways as the union of two distinct monocolored sets. If GCH holds, for every such coloring there is a finite set that can be written at least 1/2 ∑i=1n (nn+i) (in) ways as the union of two sets with the same color.
AB - It is consistent for every 1 ≤ n < ω that 2ω = ωn and there is a function F : [ωn]<ω → ω such that every finite set can be written in at most 2n-1 ways as the union of two distinct monocolored sets. If GCH holds, for every such coloring there is a finite set that can be written at least 1/2 ∑i=1n (nn+i) (in) ways as the union of two sets with the same color.
KW - Axiomatic set theory
KW - Combinatorial set theory
KW - Independence proofs
UR - http://www.scopus.com/inward/record.url?scp=33645946056&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-96-03450-8
DO - 10.1090/s0002-9939-96-03450-8
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AN - SCOPUS:33645946056
SN - 0002-9939
VL - 124
SP - 3501
EP - 3505
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 11
ER -