well orderings


A total ordering R on a set S is a well ordering if every subset of S has a smallest element. Well orderings are important because one can use a generalization of mathematical induction known as transfinite induction. The canonical example is the ordinal numbers.


This concept has the prerequisites:


  • Know what it means for a relation to be a well ordering
  • Know the transfinite induction principle and why it is justified
  • Be able to define functions using transfinite recursion

Core resources (read/watch one of the following)


Notes on Set Theory (2013)
Lecture notes for a course on axiomatic set theory.
Author: Henry Cohn


See also

-No Additional Notes-