Structures of degrees of negative representations of linear orders

The structures of partially ordered sets of degrees of negative and positive representability of linear orders are studied. The focus is on the negative representability of linear orders and orders with endomorphisms. In particular, for these structures established the existence of incomparable, maximal and minimal degrees, infinite chains and anti-chains, and also considered the connection with the concepts of the reducibility of enumerartions, splittable degrees and positive representations.