Z_2 2002-08-17 23:31:53 2006-12-17 16:20:41 Definition second order arithmetic % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here %\PMlinkescapeword{theory} $Z_2$ is the full system of second order arithmetic, that is, the full theory of numbers and sets of numbers. It is sufficient for a great deal of mathematics, including much of number theory and analysis. The axioms defining successor, addition, multiplication, and comparison are the same as those of PA. $Z_2$ adds the full induction axiom and the full comprehension axiom.