Ordinals and Cardinals

Andrei Popescu

1 September 2009

Abstract

We develop a basic theory of ordinals and cardinals in Isabelle/HOL, up to the point where some cardinality facts relevant for the ``working mathematician" become available. Unlike in set theory, here we do not have at hand canonical notions of ordinal and cardinal. Therefore, here an ordinal is merely a well-order relation and a cardinal is an ordinal minim w.r.t. order embedding on its field.
BSD License

Change history

[2012-09-25] This entry has been discontinued because it is now part of the Isabelle distribution.

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@article{Ordinals_and_Cardinals-AFP,
  author  = {Andrei Popescu},
  title   = {Ordinals and Cardinals},
  journal = {Archive of Formal Proofs},
  month   = September,
  year    = 2009,
  note    = {\url{http://isa-afp.org/entries/Ordinals_and_Cardinals.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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