FastSet is a distributed protocol for decentralized finance and settlement, which is inspired from both actors and blockchains. Account holders cooperate by making claims, which can include payments, holding and transferring assets, accessing and updating shared data, medical records, digital identity, and mathematical theorems, among others. The claims are signed by their owners and are broadcast to a decentralized network of validators, which validate and settle them. Validators replicate the global state of the accounts and need not communicate with each other. In sharp contrast to blockchains, strong consistency is purposely given up as a requirement. Yet, many if not most of the blockchain benefits are preserved, while capitalizing on actor's massive parallelism. The protocol is proved to be correct, despite its massively parallel nature.