Uniform inseparability in explicit mathematics
We deal with ontological problems concerning basic systems of explicit mathematics, as
formalized in Jäger's language of types and names. We prove a generalized inseparability
lemma, which implies a form of Rice's theorem for types and a refutation of the strong power
type axiom POW+. Next, we show that POW+ can already be refuted on the basis of a weak
uniform comprehension without complementation, and we present suitable optimal
refinements of the remaining results within the weaker theory.
formalized in Jäger's language of types and names. We prove a generalized inseparability
lemma, which implies a form of Rice's theorem for types and a refutation of the strong power
type axiom POW+. Next, we show that POW+ can already be refuted on the basis of a weak
uniform comprehension without complementation, and we present suitable optimal
refinements of the remaining results within the weaker theory.
We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW+. Next, we show that POW+ can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.
Cambridge University PressShowing the best result for this search. See all results