依赖的梦：叙述类型

摘要：

我们研究了一般相依理论的模型类。我们继续数学。LO/0702292特别是调查所谓的“类型分解”;论文是什么成立稳定的理论和Th（Q，<）成立依赖的理论。另一种说法是：我们必须考虑足够小的邻域，并使用合理的可定义类型来分析类型。我们注意到，在没有读数的情况下，结果不稳定。首先，与“稳定性谱”平行的是“类型的重新叙述”，即假设lambda = lambda^{< lambda}足够大，M是基数为lambda的T的饱和模型，设粗体S_{aut}（M）是M上直到共轭的完全类型的数量，即当M的某个自同构将p映射到q时，我们标识p，q。而对于独立的T，这个数是2 ^lambda，对于相关的T，这个数是<= lambda，而且它是<=|阿尔法|当lambda = aleph_alpha时，为^{ |T| }。第二，对于稳定的理论，“存在大量的不可分辨性”，一个“太好的不可分辨存在定理”说，例如，如果类型tp（d_beta ; {d_beta：beta < alpha}）对于alpha < kappa = cf（kappa）和kappa > 2^{ |T| }是递增的，那么<d_alpha：alpha in S>对于某个稳定的S子集k是不可分辨的。第三，对于稳定的T，一个模型是kappa饱和的当且仅当它是aleph_epsilon饱和的，并且基数< kappa的每一个无限不可分辨的（元素）集都可以增加。我们在这里证明一个类比。第四，对于S（M）中的p，M的外部可定义子集上扩展p的超滤子的数目有一个绝对界2^{ |T| }。将我们自己限制在一个phi（x，y），这个数是有限的，有一个绝对值（取决于T和phi）。

英文摘要：

We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent theories. Another way to say this is: we have to look at small enough neighborhood and use reasonably definable types to analyze a type. We note the results understable without reading. First, a parallel to the "stability spectrum", the "recounting of types", that is assume lambda = lambda^{< lambda} is large enough, M a saturated model of T of cardinality lambda, let bold S_{aut}(M) be the number of complete types over M up to being conjugate, i.e. we identify p,q when some automorphism of M maps p to q . Whereas for independent T the number is 2^lambda, for dependent T the number is <= lambda moreover it is <= | alpha |^{|T|} when lambda = aleph_alpha. Second, for stable theories "lots of indiscernibility exists" a "too good indiscernible existence theorem" saying, e.g. that if the type tp (d_beta ; {d_beta : beta < alpha}) is increasing for alpha < kappa = cf(kappa) and kappa > 2^{|T|} then <d_alpha : alpha in S> is indiscernible for some stationary S subseteq kappa. Third, for stable T,a model is kappa-saturated iff it is aleph_epsilon-saturated and every infinite indiscernible set (of elements) of cardinality < kappa can be increased. We prove here an analog. Fourth, for p in S(M), the number of ultrafilters on the outside definable subsets of M extending p has an absolute bound 2^{|T|} . Restricting ourselves to one phi(x, y), the number is finite, with an absolute found (well depending on T and phi).

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