homogeneous

Let $L$ be a first order language. Let $M$ be an $L$-structure. Then we say $M$ is homogeneous if the following holds:

if$\sigma$ is an isomorphism between finite substructures of $M$, then $\sigma$ extends to an automorphism of $M$.

Title	homogeneous
Canonical name	Homogeneous
Date of creation	2013-03-22 13:23:13
Last modified on	2013-03-22 13:23:13
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	5
Author	mathcam (2727)
Entry type	Definition
Classification	msc 03C50
Related topic	ExampleOfUniversalStructure
Related topic	RandomGraph