Bob A. Dumas

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2ranked-venue papers
2as first author
1since 2021 · last 2024
0000-0002-7058-3518ORCID · corroborated

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Theory of computation · 2 · 2 first-author · 1 since 2021
YearPublicationVenuePosition
2024 Discontinuous Homomorphisms of with
abstract
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.
Bob A. Dumas
J. Symb. Log.1
2009 Order-isomorphic eta1-orderings in Cohen extensions
Bob A. Dumas
Ann. Pure Appl. Log.1