Nontrivial twisted sums for finite height spaces under Martin's Axiom

We show that if we assume Martin’s Axiom, then there exists a nontrivial twisted sum of c_0 and C(K), for every compact space K with finite height and weight at least continuum. This result settles the problem of existence of nontrivial twisted sums of c_0 and C(K), for finite height spaces K, under Martin’s Axiom.