You may also want to search for Berliner, Ukraine in The JewishGen FamilyFinder (JGFF) . You will need to create and login with a JewishGen user account in order to see their information, but their website is free to use and extremely helpful.
Gesher Galicia is a non-profit organization carrying out Jewish genealogical and historical research on Galicia, formerly a province of Austria-Hungary and today divided between southeastern Poland and western Ukraine. The research work includes the indexing of archival vital records and census books, Holocaust-period records, Josephine and Franciscan cadastral surveys, lists of Jewish taxpayers, and records of Galician medical students and doctors - all added to our searchable online database. In addition, we reproduce regional and cadastral maps for our online Map Room. We conduct educational research and publish a quarterly research journal, the Galitzianer.