Title: Discontinuous Homomorphisms of $C(X)$ with $2^{\aleph_0}>\aleph_2$,
Abstract: 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 reals
and $G$ is $P$-generic over $M$. In $M$ we construct a function between sets of
terms in the forcing language, that interpreted in $M[G]$ is an $\mathbb
R$-linear order-preserving monomorphism from the finite elements of an
ultrapower of the reals, over a non-principal ultrafilter on $\omega$, into the
Esterle 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 continuous
real-valued functions on $X$. For $n\in \mathbb N$, If $M$ contains a
simplified $(\omega_1,n)$-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 $X$.