This paper presents a simple framework unifying a family of consensus algorithms that can tolerate process crash failures and asynchronous periods of the network, also called indulgent consensus algorithms. Key to the framework is a new abstraction we introduce here, called Alpha, and which precisely captures consensus safety. Implementations of Alpha in shared memory, storage area network, message passing and active disk systems are presented, leading to directly derived consensus algorithms suited to these communication media. The paper also considers the case where the number of processes is unknown and can be arbitrarily large.