Unreliable failure detectors are mechanisms providing information about process failures, that allow solving several problems in asynchronous systems, e.g., Consensus. A particular class of failure detectors, Omega, provides an eventual leader election functionality. This paper addresses the implementation of Omega in the crash-recovery failure model. Recently we have proposed an algorithm assuming that eventually the correct process with the smallest identifier and minimum incarnation number can communicate timely with the rest of processes. Here we propose two Omega algorithms which assume only that processes are reachable from some correct process, independently of its identifier and incarnation number. The first one requires the membership to be known a priori, while the second one relaxes this assumption too.