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- Title
DISCONTINUOUS HOMOMORPHISMS OF $C(X)$ WITH $2^{\aleph _0}>\aleph _2$.
- Authors
DUMAS, BOB A.
- 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.
- Subjects
EXPONENTS; HAUSDORFF spaces; COMMERCIAL space ventures; POWER series; HOMOMORPHISMS; ALGEBRA
- Publication
Journal of Symbolic Logic, 2024, Vol 89, Issue 2, p665
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2024.28