Orbit-finite System of Linear Equations

An orbit-finite system of linear equations is a system of linear equations where the equations and the variables used in them are possibly infinite but are finite up to certain symmetries. I will start with a brief description of atoms and orbit-finite sets. Then I will define vector spaces over orbit-finite sets and try to show using an example why these have orbit-finite bases. In the end, I will define orbit-finite systems of linear equations and discuss our recent results regarding them.