一个替代来回
An alternative to back-and-forth
摘要：
我们展示了如何Rasiowa-Sikorski引理简化，在某种意义上说，证明的结果，利用称为来回的技术，往往导致不很说明性的参数。前两节试图展示已知结果的一个简单和一个复杂的证明，希望读者能欣赏到这些论证是如何结束的，在我们看来，比经典文献中的论证要清楚得多。最后一节展示了同样的技术如何适用于通常被认为与集合论相距甚远的领域，在本例中是图论。第一和第二部分是基于我的学士论文，在罗伯托·皮查多·门多萨博士的指导下，我深深感谢他的建议和对本书的修改。本文中提到的所有结果都是众所周知的，然而，据我们所知，最后两节中的证明是原创的。
英文摘要：
We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple and one complicated proofs of known results, in the hopes that the reader appreciates how the arguments end up, in our view, considerably clearer than those found in classic literature. The final section shows how the same techniques can be adapted to areas commonly considered distant to Set Theory, in this instance, Graph Theory. Sections one and two are based on my bachelor thesis, under the direction of Dr. Roberto Pichardo Mendoza, whom I deeply thank for his advice and revision of this work. All results mentioned in this paper are well known, however, as far as we know, the proofs in the last two sections are original.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
