On matroid properties definable in the MSO logic

Abstract

It has been proved by the author that all matroid properties definable in the monadic second-order (MSO) logic can be recognized in polynomial time for matroids of bounded branch-width which are represented by matrices over finite fields. (This result extends so called MS 2-theorem of graphs by Courcelle and others.) In this work we review the MSO theory of finite matroids and show some interesting matroid properties which are MSO-definable. In particular, all minor-closed properties are recognizable in such way.