Borel sets without perfectly many overlapping translations  

Andrzej Rosłanowski,

Saharon Shelah


We study the existence of Borel sets B  2 admitting a sequence  :  <  of distinct elements of 2 such that (+B)( +B)  6 for all ,  <  but with no perfect set of such ’s. Our result implies that under the Martin Axiom, if  < c,  < 1 and 3   < , then there exists a  02 set B  2 which has  many pairwise 2–nondisjoint translations but not a perfect set of such translations. Our arguments closely follow Shelah [7, Section 1].

AMS subject classification: Primary 03E35; Secondary 03E15, 03E50.


Słowa kluczowe: Forcing, Borel sets, Cantor space, perfect set of overlapping translations, non-disjointness rank

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