# Ordinals and Cardinals

 Title: Ordinals and Cardinals Author: Andrei Popescu (a /dot/ popescu /at/ mdx /dot/ ac /dot/ uk) Submission date: 2009-09-01 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. Change history: [2012-09-25]: This entry has been discontinued because it is now part of the Isabelle distribution. BibTeX: ```@article{Ordinals_and_Cardinals-AFP, author = {Andrei Popescu}, title = {Ordinals and Cardinals}, journal = {Archive of Formal Proofs}, month = sep, year = 2009, note = {\url{http://isa-afp.org/entries/Ordinals_and_Cardinals.html}, Formal proof development}, ISSN = {2150-914x}, }``` License: BSD License