The fundamental tension between availability and consistency shapes the design of distributed storage systems. Classical results capture extreme points of this trade-off: the CAP theorem shows that strong models like linearizability preclude availability under partitions, while weak models like causal consistency remain implementable without coordination. These theorems apply to simple read-write interfaces, leaving open a precise explanation of the combinations of object semantics and consistency models that admit available implementations. This paper develops a general semantic framework in which storage specifications combine operation semantics and consistency models. The framework encompasses a broad range of objects (key-value stores, counters, sets, CRDTs, and SQL databases) and consistency models (from causal consistency and sequential consistency to snapshot isolation and bounded staleness). Within this framework, we prove the Arbitration-Free Consistency (AFC) theorem, showing that an object specification within a consistency model admits an available implementation if and only if it is arbitration-free , that is, it does not require a total arbitration order to resolve visibility or read dependencies. The AFC theorem unifies and generalizes previous results, revealing arbitration-freedom as the fundamental property that delineates coordination-free consistency from inherently synchronized behavior.

@article{paperbot3854,
  title = {Arbitration-Free Consistency Is Available (and Vice Versa)},
  author = {Hagit Attiya and Constantin Enea and Enrique Román-Calvo},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {10},
  number = {POPL},
  year = {2026},
  doi = {10.1145/3776683}
}