Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely. Starting from Cover's theorem, which guarantees such behavior for membership in a countable set of candidate means, we ask a sharper question: \emph{which sets actually admit computable sequential decision procedures with finitely many errors?} We answer this optimally by giving a complete characterization both necessary and sufficient of the subsets of $\Q$ that admit a computable finite-error sequential membership test. We further extend the characterization to any \emph{effectively presented} countable family of real means, exactly the setting in which Cover's identification rule can be implemented computably. Beyond the technical boundary, the results clarify within a precise probabilistic setting what it can mean for inquiry to ``converge to the truth,'' and they formalize a limit to which empirical methods can be expected to succeed when only eventual stabilization (rather than fixed-time guarantees) is demanded. keywords: Cover's theorem, sequential decision procedures, finite error learning, limit computability, $Δ^0_2$ sets.

翻译：序贯假设检验旨在寻求随数据到达而更新的决策规则。一个自然的目标是\emph{最终正确性}：规则可能在早期改变观点，但几乎必然地只能做出有限次错误决策。从Cover定理（该定理保证了关于可数候选均值集合的成员性具有这一性质）出发，我们提出一个更尖锐的问题：\emph{哪些集合实际上允许具有有限错误次数的可计算序贯决策过程？}我们通过给出$\Q$子集上存在可计算有限错误序贯成员性检验的充要条件的完整刻画，实现了对这一问题的优化回答。进一步地，我们将该刻画推广到任意\emph{有效呈现}的可数实均值族——这正是Cover识别规则可被可计算实现的确切场景。除技术边界外，这些结果在精确的概率框架下阐明了探究过程“收敛于真理”的可能含义，并形式化地刻画了当仅要求最终稳定性（而非固定时间保证）时，经验方法可预期成功的极限。关键词：Cover定理，序贯决策过程，有限错误学习，极限可计算性，$Δ^0_2$集合。