This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a model of a theory [Formula: see text] in a countable language. More precisely, we find a theory in a countable language such that the set of types omissible in some of its models is a complete [Formula: see text] set and a complete theory in a countable language such that the set of types omissible in some of its models is a complete [Formula: see text] set. Two more unexpected examples are given: (i) a complete theory [Formula: see text] and a countable set of types such that each of its finite sets is jointly omissible in a model of [Formula: see text], but the whole set is not and (ii) a complete theory and two types that are separately omissible, but not jointly omissible, in its models.

中文翻译：

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在度量结构的逻辑中省略类型

本文是关于省略 Ben Yaacov、Berenstein、Henson 和 Usvyatsov 引入的度量结构逻辑中的类型。虽然在可数完全理论的某些模型中完全类型是可省略的当且仅当它不是主要的，但对于 Ben Yaacov 的结果的不完全类型来说，这不是真的。我们证明，在可数语言的理论模型[公式：见文本]中，没有简单的测试来确定一个类型是否可省略。更准确地说，我们在可数语言中找到了一个理论，使得在它的某些模型中可省略的类型集是一个完整的 [公式：见正文] 集，并且在可数语言中找到了一个完整的理论，使得在某些模型中可省略的类型集它的模型是一个完整的[公式：见正文]集。给出了另外两个意想不到的例子：（i）一个完整的理论[公式：