Theories without the tree property of the second kind
Theories without the tree property of the second kind
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没有第二类树性质的理论
DOI：
10.1016/j.apal.2013.10.002
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Chernikov
中科院分区：
文献类型：
--
作者：
A. Chernikov
我们开始系统地研究一类没有第二类树性质的理论- ntp 2。最重要的是，我们表明：在任意理论中，负担是“次乘法”的（特别是，如果一个理论有TP 2，那么就有一个公式，其中一个变量见证了这一点）；NTP 2等价于广义的Kim引理和ist-weight的有界性；任意理论中一个类型的dp-rank是由该类型的相互不可分辨的实现序列来证明的，在加入一些参数之后——因此任何理论中一个1类型的dp-rank总是由单例序列来证明；在NTP 2理论中，简单类型是共简单的，其特征是共独立定理，并且在简单类型和任意元素的实现之间的分叉满足完全对称；一个特征为（0,0）的Henselian值域是NTP 2（强，有限负荷）当且仅当剩余域是NTP 2（剩余域和值群分别是强，有限负荷），所以特别地p-基的任何超积都是NTP 2；将泛型谓词添加到几何NTP 2理论中可以保留NTP 2。
We initiate a systematic study of the class of theories without the tree property of the second kind—NTP 2. Most importantly, we show: the burden is “sub-multiplicative” in arbitrary theories (in particular, if a theory has TP 2 then there is a formula with a single variable witnessing this); NTP 2 is equivalent to the generalized Kimʼs lemma and to the boundedness of ist-weight; the dp-rank of a type in an arbitrary theory is witnessed by mutually indiscernible sequences of realizations of the type, after adding some parameters—so the dp-rank of a 1-type in any theory is always witnessed by sequences of singletons; in NTP 2 theories, simple types are co-simple, characterized by the co-independence theorem, and forking between the realizations of a simple type and arbitrary elements satisfies full symmetry; a Henselian valued field of characteristic (0, 0) is NTP 2 (strong, of finite burden) if and only if the residue field is NTP 2 (the residue field and the value group are strong, of finite burden respectively), so in particular any ultraproduct of p-adics is NTP 2; adding a generic predicate to a geometric NTP 2 theory preserves NTP 2.
关于 NIP 和不变测度
影响因子：
2.6
作者：
Pillay A
通讯作者：
Pillay A