  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.
