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Assume that $M$ is a c.t.m. of $ZFC+CH$ containing a simplified$(\omega_1,2)$-morass, $P\in M$ is the poset adding $\aleph_3$ generic realsand $G$ is $P$-generic over $M$. In $M$ we construct a function between sets ofterms in the forcing language, that interpreted in $M[G]$ is an $\mathbbR$-linear order-preserving monomorphism from the finite elements of anultrapower of the reals, over a non-principal ultrafilter on $\omega$, into theEsterle algebra of formal power series. Therefore it is consistent that$2^{\aleph_0}=\aleph_3$ and, for any infinite compact Hausdorff space $X$,there exists a discontinuous homomorphism of $C(X)$, the algebra of continuousreal-valued functions on $X$. For $n\in \mathbb N$, If $M$ contains asimplified $(\omega_1,n)$-morass, then in the Cohen extension of $M$ adding$\aleph_n$ generic reals there exists a discontinuous homomorphism of $C(X)$,for any infinite compact Hausdorff space $X$.

Discontinuous Homomorphisms of $C(X)$ with $2^{\aleph_0}>\aleph_2$