随机偏序的约化
Reducts of the random partial order
摘要：
我们确定，直到一阶互定义的等价，所有的结构是一阶定义的随机偏序。事实证明，这些结构正好可以分为五个等价类。我们通过证明恰好存在五个包含随机偏序的自同构群的封闭置换群来实现这一结果，从而暴露了该结构的所有对称性。我们的分类与以前类似的分类相一致，例如在随机图中可定义的结构或有理数的顺序;它还为Simon Thomas的猜想提供了进一步的证据，该猜想指出，在有限关系语言中，在同构结构中可定义的结构的数量，直到一阶可相互定义性，总是有限的。我们采用的方法是基于拉姆齐理论分析的功能作用于随机偏序，这使我们能够找到这样的功能模式，并使他们访问有限的组合参数。
英文摘要：
We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve this result by showing that there exist exactly five closed permutation groups which contain the automorphism group of the random partial order, and thus expose all symmetries of this structure. Our classification lines up with previous similar classifications, such as the structures definable in the random graph or the order of the rationals; it also provides further evidence for a conjecture due to Simon Thomas which states that the number of structures definable in a homogeneous structure in a finite relational language is, up to first-order interdefinability, always finite. The method we employ is based on a Ramsey-theoretic analysis of functions acting on the random partial order, which allows us to find patterns in such functions and make them accessible to finite combinatorial arguments.
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