AI 中文总结
该研究证明可数施泰纳三元系的同构关系是博雷尔完备的，通过构造保持自同构的博雷尔归约完成证明，拓展了博雷尔完备性在组合结构中的相关结论。
AI 中文摘要
我们证明可数施泰纳三元系的同构关系是博雷尔完备的，即任意可数结构的同构关系可博雷尔归约到可数施泰纳三元系的同构关系。为证明该结论，我们构造了从可数图到可数施泰纳三元系的忠实博雷尔归约，即博雷尔映射θ，将每个可数图G关联到可数施泰纳三元系θ(G)，使得G同构于G'当且仅当θ(G)同构于θ(G')，且θ保持自同构，即Aut(G)同构于Aut(θ(G))。
英文摘要
We show that the isomorphism relation for countable Steiner triple systems is Borel complete, that is, the isomorphism relation for arbitrary countable structures is Borel reducible to that for countable Steiner triple systems. To prove it, we construct a faithful Borel reduction from countable graphs to countable Steiner triple systems, that is, a Borel assignment $θ$ that associates every countable graph $G$ with a countable Steiner triple system $θ(G)$ so that $G\cong G'$ if and only if $θ(G)\congθ(G')$. Moreover, $θ$ preserves automorphisms which means that $\mathrm{Aut}(G)\cong\mathrm{Aut}(θ(G))$.
Comments16 pages, 2 figures
