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. Gesher Galicia is also organized for the purpose of maintaining networking and online discussion groups and to promote and support Jewish heritage preservation work in the areas of the former Galicia.