论文标题
局部紧凑的波兰度量结构的同构
Isomorphism of locally compact Polish metric structures
论文作者
论文摘要
我们研究了局部紧凑的波兰度量结构的鲍尔类别的同构关系。我们证明，此类类别上的同构总是可以通过可数结构（等效地：可还原为图同构的Borel）进行分类，这特别暗示，局部紧凑的波兰度量空间的等距是可还原为图等形态的borel。我们表明，潜在的$ \pmbπ^0_ {α+1} $同构关系是可以降低到遗传上可计数的等级$α$，$α\ geq 2 $的平等的borel。我们还研究了Hjorth-同顺态游戏的近似，并制定了一种根据可数结构排除分类性的条件。
We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism), which implies, in particular, that isometry of locally compact Polish metric spaces is Borel reducible to graph isomorphism. We show that potentially $\pmbΠ^0_{α+1}$ isomorphism relations are Borel reducible to equality on hereditarily countable sets of rank $α$, $α\geq 2$. We also study approximations of the Hjorth-isomorphism game, and formulate a condition ruling out classifiability by countable structures.
