Some Case Studies in Algebra Motivated by Abstract Problems of Language
This thesis concerns three different topics. The first has to do with axiomatizing the universal theory of certain classes of multisorted algebras arising from intersection, union, and other first order operations on relations. The second has to do with axiomatizing certain classes of actions arising from intersection and union, and axiomatizing certain classes of posets arising from actions arising from intersection. The third has to do with understanding under what conditions morphisms between two structures can be finitely determined.