In this chapter, we shall introduce a set-theoretic axiom, known as Martin’s Axiom, which is independent of ZFC. In the presence of the Continuum Hypothesis, Martin’s Axiom becomes trivial, but if the Continuum Hypothesis fails, then Martin’s Axiom becomes an interesting combinatorial statement as well as an important tool in Combinatorics. Furthermore, Martin’s Axiom provides a good introduction to the forcing technique which will be introduced in the next chapter.
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