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On completely Ramsey sets. (English) Zbl 0632.04005
We consider completely Ramsey sets. Our main result says that the union of less than $$\kappa (N^*)$$ of completely Ramsey sets is completely Ramsey and the union of $$\kappa (N^*)$$ of completely Ramsey sets can be a set which is not completely Ramsey.

##### MSC:
 3e+15 Descriptive set theory
##### Keywords:
completely Ramsey sets
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