Abstract

We show that several weakenings of the Cauchy condition are all equivalent under the assumption of countable choice, and investigate to what extent choice is necessary. We also show that the syntactically reminiscent notion of metastability allows similar variations, but is empty in terms of its constructive content.1¹

中文翻译：

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柯西性和亚稳性的概念

我们证明柯西条件的几个弱点在可数选择的假设下都是等效的，并研究选择的必要程度。我们还表明，在语法上让人联想到亚稳态的概念允许类似的变化，但就其建设性内容而言是空的。^1个