  Eventual consistency of replicated data supports concurrent updates, reduces
latency and improves fault tolerance, but forgoes strong consistency.
Accordingly, several cloud computing platforms implement eventually-consistent
data types. The set is a widespread and useful abstraction, and many replicated
set designs have been proposed. We present a reasoning abstraction, permutation
equivalence, that systematizes the characterization of the expected concurrency
semantics of concurrent types. Under this framework we present one of the
existing conflict-free replicated data types, Observed-Remove Set. Furthermore,
in order to decrease the size of meta-data, we propose a new optimization to
avoid tombstones. This approach that can be transposed to other data types,
such as maps, graphs or sequences.
