"Partition theorems for uncountable expanded trees"Shelah, SaharonWe look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on subtrees of $ {}^{ \kappa g}2 $ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding to preserve the height of the tree. We get consistency results without large cardinals. On background see for example Dobrinen-Shelah. The intention is to apply it to model theoretic problems. |
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