When a linear order has an order preserving surjection onto each of its suborders, we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is a [Formula: see text]-complete set. Using hypotheses beyond ZFC, we prove the existence of uncountable strongly surjective orders.

中文翻译：

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线性顺序：当可嵌入性和同态一致时

当一个线性阶在它的每个子阶上都有一个保阶满射，我们说它是强满射的。我们证明了可数强满射线性阶的集合是[公式：见正文]-完备集。使用 ZFC 之外的假设，我们证明了不可数强满射阶的存在。