论文标题
关于小分析关系
On small analytic relations
论文作者
论文摘要
与连续降低性或注入性连续降低性的概念相比，我们研究了波兰空间上的分析二元关系类别。特别是，我们表征当本地可计数的Borel关系为$σ$ 0 $ξ$（或$π$ 0 $ 0 $ξ$）时，当$ξ$ $ \ ge $ 3时，通过提供具体的有限抗基础。当$ξ$ = 1时，我们给出了类似的特征，当$ξ$ = 2时，我们提供了由本地可数的borel关系制成的大小连续体的混凝土抗，在非 - $σ$ 0 2（或非$π$ 0 2）之间的关系最小值。最后一个结果的证明使我们能够加强由于拓扑拉西理论中关于理性数字空间的鲍姆加特纳引起的结果。我们证明，当$ξ$ = 2中的2 $ = 2时，积极的结果会产生。我们在不必要的局部可计数案例中给出了总体上的积极结果，并具有另一个合适的无环性假设。我们为无数分析关系类别提供了具体的有限抗基础。最后，我们从积极的结果中得出图形的一些敌基依据（大部分时间1或2）。
We study the class of analytic binary relations on Polish spaces, compared with the notions of continuous reducibility or injective continuous reducibility. In particular, we characterize when a locally countable Borel relation is $Σ$ 0 $ξ$ (or $Π$ 0 $ξ$), when $ξ$ $\ge$ 3, by providing a concrete finite antichain basis. We give a similar characterization for arbitrary relations when $ξ$ = 1. When $ξ$ = 2, we provide a concrete antichain of size continuum made of locally countable Borel relations minimal among non-$Σ$ 0 2 (or non-$Π$ 0 2) relations. The proof of this last result allows us to strengthen a result due to Baumgartner in topological Ramsey theory on the space of rational numbers. We prove that positive results hold when $ξ$ = 2 in the acyclic case. We give a general positive result in the non-necessarily locally countable case, with another suitable acyclicity assumption. We provide a concrete finite antichain basis for the class of uncountable analytic relations. Finally, we deduce from our positive results some antichain basis for graphs, of small cardinality (most of the time 1 or 2).
