Weyl’s Predicative Classical Mathematics as a Logic-Enriched Type Theory

  • Robin Adams
  • Zhaohui Luo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4502)

Abstract

In Das Kontinuum, Weyl showed how a large body of classical mathematics could be developed on a purely predicative foundation. We present a logic-enriched type theory that corresponds to Weyl’s foundational system. A large part of the mathematics in Weyl’s book — including Weyl’s definition of the cardinality of a set and several results from real analysis — has been formalised, using the proof assistant Plastic that implements a logical framework. This case study shows how type theory can be used to represent a non-constructive foundation for mathematics.

Keywords

logic-enriched type theory predicativism formalisation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Robin Adams
    • 1
  • Zhaohui Luo
    • 1
  1. 1.Dept of Computer Science, Royal Holloway, Univ of London 

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