<![CDATA[WUJ]]><![CDATA[info@ejournals.eu]]>http://www.ejournals.eu/20191212ejournals.eu.article.1443903010610.4467/20842589RM.19.001.1064920<![CDATA[Forcing, Borel sets, Cantor space, perfect set of overlapping translations, non-disjointness rank]]>00ED031001Number10102<![CDATA[Reports on Mathematical Logic]]>03<![CDATA[2019]]>01<![CDATA[Number 54]]>1A01<![CDATA[Andrzej RosÅ‚anowski]]>2A01<![CDATA[Saharon Shelah]]>0101<![CDATA[Borel sets without perfectly many overlapping translations
]]>01en00303020PLN03<![CDATA[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.
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