论文标题
难以分辨的子空间和最少的宽类型
Indiscernible Subspaces and Minimal Wide Types
论文作者
论文摘要
我们开发了在巴拉奇空间扩展的连续理论中开发了不可见作用的子空间的机制，这表明任何这样的理论都有难以置信的子空间，因此是不可见的。我们通过表明（可能不稳定的）最小宽$ p $的一系列实现是$ p $的莫利序列，并且仅当它是$ p $中不可见作的子空间的正顺序基础时，我们扩展了Shelah和Usvyatsov的结果。我们还举了一个例子，表明最少的宽类型通常没有类型可定义的不可化的子空间（回答Shelah和UsvyAtsov的问题），以及一个例子，表明我们的结果对于非最小程度较大的类型，即使以$ω$稳定的理论为单位。
We develop the machinery of indiscernible subspaces in continuous theories of expansions of Banach spaces, showing that any such theory has an indiscernible subspace and therefore an indiscernible set. We extend a result of Shelah and Usvyatsov by showing that a sequence of realizations of a (possibly unstable) minimal wide type $p$ is a Morley sequence in $p$ if and only if it is the orthonormal basis of an indiscernible subspace in $p$. We also give an example showing that minimal wide types do not generally have type-definable indiscernible subspaces (answering a question of Shelah and Usvyatsov), as well as an example showing that our result fails for non-minimal wide types, even in $ω$-stable theories.
