homogeneous Homogeneous4 2003-01-24 11:30:30 2005-05-17 09:57:50 Definition % 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 Let $L$ be a first order language. Let $M$ be an $L$-structure. Then we say $M$ is {\em homogeneous} if the following holds: if$\sigma$ is an isomorphism between finite substructures of $M$, then $\sigma$ extends to an automorphism of $M$.