Forcing axioms are axioms of set theory that assert that certain existential statements are absolute between the universe \(V\) of all sets and its (ideal) forcing extensions, i.e., some existential statements that hold in some forcing extensions of \(V\) are already true in \(V\). The first forcing axiom was formulated by Donald Martin in the wake of the Solovay-Tennenbaum proof of the consistency of Suslin’s Hypothesis, and is now known as Martin’s Axiom (MA). Before we state it, let us say that a partial ordering is a non-empty set \(P\) together with a binary relation \(\leq\) on \(P\) that is reflexive and transitive. Two elements, \(p\) and \(q\), of \(P\) are called compatible if there exists \(r\in P\) such that \(r\leq p\) and \(r\leq q\). An antichain of \(P\) is a subset of \(P\) whose elements are pairwise-incompatible. A partial ordering \(P\) is called ccc if every antichain of \(P\) is countable. A non-empty subset \(G\) of \(P\) is called a filter if (i) every two elements of \(G\) are compatible, and (ii) if \(p\in G\) and \(p\leq q\), then also \(q\in G\). Finally, a subset \(D\) of \(P\) is called dense if for every \(p\in P\) there is \(q\in D\) such that \(q\leq p\).