We show that there is a [Formula: see text]-model of second-order arithmetic in which the choice scheme holds, but the dependent choice scheme fails for a [Formula: see text]-assertion, confirming a conjecture of Stephen Simpson. We obtain as a corollary that the Reflection Principle, stating that every formula reflects to a transitive set, can fail in models of [Formula: see text]. This work is a rediscovery by the first two authors of a result obtained by the third author in [V. G. Kanovei, On descriptive forms of the countable axiom of choice, Investigations on nonclassical logics and set theory, Work Collect., Moscow, 3-136 (1979)].

中文翻译：

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满足交流但不满足直流的二阶算术模型

我们证明了存在选择方案成立的二阶算术[公式：参见文本]-模型，但是对于[公式：参见文本]-断言，从属选择方案失败，证实了斯蒂芬辛普森的猜想。作为一个推论，我们得到反射原理，说明每个公式都反映到一个传递集，在[公式：见文本]的模型中可能会失败。这项工作是前两位作者对第三位作者在 [VG Kanovei，关于选择的可数公理的描述形式，非经典逻辑和集合论的调查，Work Collect.，莫斯科，3-136 (1979)]。