When can a learner make only finitely many prediction errors along every infinite sequence labeled by a fixed, unknown hypothesis?
We characterize this form of consistency for arbitrary binary hypothesis classes in ZFC, without requiring a uniform mistake bound.
The characterization uses a single linear order on finite realizable traces.
Each trace selects its least subtrace, and the order must satisfy two conditions:
- conflicting traces select different subtraces,
- and the order is well-founded on the traces of each fixed target.
These conditions induce a learner whose selected evidence decreases on every mistake.
Conversely, a consistent learner yields such an order through canonical mistake transcripts and the Kleene--Brouwer ordering.
The result provides a representation of consistent prediction by finite evidence, answering a question of Lu (2024).