超虚元与预完备化的正合性
Hyperimaginaries and Exactness of the Pro-Completion
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中文总结 AI 辅助
该研究将一阶理论中超虚元的消去与句法范畴预完备化的正合性关联，还刻画了heq构造，推广了Makkai的相关结果。
中文摘要 AI 辅助
给定完全一阶理论$T$，我们通过$T$的句法范畴$\textrm{def}(T)$的预完备化$\textrm{Pro}(\textrm{def}(T))$的正合性刻画$T$中超虚元的消去，从而推广了Makkai将虚元消去与$\textrm{def}(T)$正合性关联的结果；同样，我们通过$\textrm{Pro}(\textrm{def}(T))$的正合完备化刻画heq构造。
英文摘要
Given a complete first-order theory $T$, we characterise elimination of hyperimaginaries in $T$ in terms of the exactness of the pro-completion $\textrm{Pro}(\textrm{def}(T))$ of the syntactic category $\textrm{def}(T)$ of $T$, thus extending Makkai's result connecting elimination of imaginaries with the exactness of $\textrm{def}(T)$. Likewise, we characterise the heq construction in terms of the exact completion of $\textrm{Pro}(\textrm{def}(T))$.
