We develop a statistical model to predict June-July-August (JJA) daily maximum 8-h average (MDA8) ozone concentrations in the eastern United States based on large-scale climate patterns during the previous spring. We find that anomalously high JJA ozone in the East is correlated with these springtime patterns: warm tropical Atlantic and cold northeast Pacific sea surface temperatures (SSTs), as...

In this note we prove the equivalence between the axiom of choice, the well ordering principle and Zorn’s lemma, and discuss to some extent how large fragment of ZF we need in order to prove the individual implications.

Zorn’s lemma is a result in set theory that appears in proofs of some non-constructive existence theorems throughout mathematics. We will state Zorn’s lemma below and use it in later sections to prove some results in linear algebra, ring theory, and group theory. In an appendix, we will give an application to metric spaces. The statement of Zorn’s lemma is not intuitive, and some of the termino...

This tutorial deals with the application of the Axiom of Choice in one of its popular disguises to objects which are of some interest in computer science (like lattices, Boolean algebras, filters and ideals, games). We discuss some common variants of this axiom such as Zorn's Lemma, Tuckey's Maximality Principle, the Well-Ordering Theorem and the Maximal Ideal Theorem; each equivalence gives ap...