Logs are defined both as a set and as a sequence

[ghareeb-falazi]

In Section 4.3.1 Transaction Receipt, the construct $R_l$ is first defined as a set (i.e., unordered and contains no repititions) and then as a "a sequence (...) a series of log entries", which indicates it is ordered and may contain repititions, i.e., the same event emitted more than once with the same arguments in one smart contract function execution.

[kodyfanz]

This is the way to lead the story from one importance to another, first when saying $R_l$ is a set, this emphasizes the importance of the uniqueness of the log elements, later when saying the sequence $R_l$ is a series of logs entries emphasizes that it is arranged in order. Logs may need to be unique (set) and also processed in specific sequence/series