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Search: authors:"Benno van den Berg"

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A Kuroda-style j-translation

A nucleus is an operation on the collection of truth values which, like double negation in intuitionistic logic, is monotone, inflationary, idempotent and commutes with conjunction. Any nucleus determines a proof-theoretic translation of intuitionistic logic into itself by applying it to atomic formulas, disjunctions and existentially quantified subformulas, as in the Gödel...

Univalent completion

We show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration.

The strength of countable saturation

In earlier work we introduced two systems for nonstandard analysis, one based on classical and one based on intuitionistic logic; these systems were conservative extensions of first-order Peano and Heyting arithmetic, respectively. In this paper we study how adding the principle of countable saturation to these systems affects their proof-theoretic strength. We will show that...

Noncommutativity as a Colimit

Benno van den Berg 0 Chris Heunen 0 0 B. van den Berg Fachbereich Mathematik, Technische Universitt Darmstadt , Darmstadt, Germany We give substance to the motto every partial algebra is the