A jury will decide whether four men accused of plotting to blow up a Bronx synagogue and a Jewish community center were induced into participating in a government-manufactured scheme designed to entrap the defendants, a federal judge ruled Wednesday.

James Cromitie maintained that a government informant infiltrated a mosque in Newburgh, N.Y., where the informant stoked Cromitie’s hatred for Jews and offered him and the other defendants huge sums of money to target synagogues and military aircraft.