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We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs ofresults that make use of the technique known as back-and-forth, often resultingin not very illustrative arguments. The first two sections seek to show onesimple and one complicated proofs of known results, in the hopes that thereader appreciates how the arguments end up, in our view, considerably clearerthan those found in classic literature. The final section shows how the sametechniques can be adapted to areas commonly considered distant to Set Theory,in this instance, Graph Theory. Sections one and two are based on my bachelorthesis, under the direction of Dr. Roberto Pichardo Mendoza, whom I deeplythank for his advice and revision of this work. All results mentioned in thispaper are well known, however, as far as we know, the proofs in the last twosections are original.

An alternative to back-and-forth