AI 中文总结
本文在ZFC中利用有限迹上的线性序刻画了一致归纳推断，通过两个序条件诱导出每次错误减少证据的学习者，并反向构造了该序，回答Lu（2024）的问题。
AI 中文摘要
学习者何时能在由固定但未知的假设标记的每条无限序列上仅犯有限次预测错误？我们在ZFC中对任意二元假设类刻画了这种一致性形式，无需统一的错误界。该刻画使用了有限可实现迹上的单一线性序。每个迹选择其最小子迹，且该序必须满足两个条件：冲突的迹选择不同的子迹，且该序在每个固定目标的迹上是良基的。这些条件诱导出一个学习者，其选择的证据在每次错误时减少。反之，一致的学习者通过规范错误记录和Kleene-Brouwer序产生这样的序。该结果提供了一致预测的有限证据表示，回答了Lu（2024）的问题。
英文摘要
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).
