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DISCONTINUOUS HOMOMORPHISMS OF 
$C(X)$ WITH 
$2^{\aleph _0}>\aleph _2$
Published online by Cambridge University Press: 15 April 2024
Abstract
Assume that M is a transitive model 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 
$2^{\aleph _0}>\aleph _2$ 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.
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
References
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