Universes in the theories of types and names

  • Markus Marzetta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 702)


In this paper we recall the basic ideas of the theories of types and names, which were introduced by Jäger and which are closely related to Feferman's systems of explicit mathematics. We start off from the elementary theory of types and names with the datatype of the natural numbers, which is equivalent to EM0 or to EM0,↾ depending on the form of induction taken. The elementary theory is extended by universes, i.e. types enjoying special closure properties, to a theory UTN. We show how new type constructions become possible in presence of the universes and prove a lower bound for its proof theoretic strength. We sketch the proof of the upper bound of the theory, which shows that UTN does not exceed the limits of predicativity.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Markus Marzetta
    • 1
  1. 1.Institut für Informatik und angewandte MathematikUniversity of BerneSwitzerland

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