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Uniform inseparability in explicit mathematics

Published online by Cambridge University Press:  12 March 2014

Andrea Cantini  and
Pierluigi Minari
Andrea Cantini
Affiliation:
Department of Philosophy, Università Degli Studi di Firenze, Via Bolognese 52, 1-50139 Firenze, Italy E-mail: cantini@mailserver.idg.fi.cnr.it
Pierluigi Minari
Affiliation:
Department of Philosophy, Università Degli Studi di Firenze, Via Bolognese 52, 1-50139 Firenze, Italy E-mail: minari@mphilos.unifi.it
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 313 - 326
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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