# 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.