当局部性遇到保存
When Locality Meets Preservation
摘要：
本文研究了Gaifman范式中一阶句子片段，即基本局部句子的正布尔组合的表达性。我们证明了它们完全匹配局部初等嵌入下保持的一阶句子，从而提供了一个新的一般保持定理，并扩展了Lós-Tarski定理。这个完整的保存结果失败，像往常一样，在有限的，我们进一步表明，自然相关的决策问题是不可判定的。在更受限制的情况下，保存下的扩展，它仍然产生新的表现良好的类的有限结构：我们证明，保存下的扩展保持当且仅当它保持局部。
英文摘要：
This paper investigates the expressiveness of a fragment of first-order sentences in Gaifman normal form, namely the positive Boolean combinations of basic local sentences. We show that they match exactly the first-order sentences preserved under local elementary embeddings, thus providing a new general preservation theorem and extending the Lós-Tarski Theorem. This full preservation result fails as usual in the finite, and we show furthermore that the naturally related decision problems are undecidable. In the more restricted case of preservation under extensions, it nevertheless yields new well-behaved classes of finite structures: we show that preservation under extensions holds if and only if it holds locally.
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