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There exist many forms of Blockchain finality conditions, from deterministic to probabilistic terminations. To favor availability against consistency in the face of partitions, most blockchains only offer probabilistic eventual finality: blocks may be revoked after being appended to the blockchain, yet with decreasing probability as they sink deeper into the chain. Other blockchains favor consistency by leveraging the immediate finality of Consensus-a block appended is never revoked-at the cost of additional synchronization. In this paper, we focus on necessary and sufficient conditions to implement a blockchain with deterministic eventual finality, which ensures that selected main chains at different processes share a common increasing prefix. This is a much weaker form of finality that allows us to provide a solution in an asynchronous system subject to unlimited number of byzantine failures. We study stronger forms of eventual finality as well and show that it is unfortunately impossible to provide a bounded displacement. By bounded displacement we mean that the (unknown) number of blocks that can be revoked from the current blockchain is bounded. This problem reduces to consensus or eventual consensus depending on whether the bound is known or not. We also show that the classical selection mechanism, such as in Bitcoin, that appends blocks at the longest chain is not compliant with a solution to eventual finality.