Zermelo’s Well-Ordering Theorem in Type Theory

  • Danko Ilik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4502)


Taking a ‘set’ to be a type together with an equivalence relation and adding an extensional choice axiom to the logical framework (a restricted version of constructive type theory) it is shown that any ‘set’ can be well-ordered. Zermelo’s first proof from 1904 is followed, with a simplification to avoid using comparability of well-orderings. The proof has been formalised in the system AgdaLight.


Initial Segment Type Theory Elimination Rule Extensional Axiom Canonical Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Danko Ilik
    • 1
  1. 1.DCS Master Programme, Chalmers University of Technology 

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