Dickson's Lemma, Higman's Theorem and Beyond: a survey of some basic results in order theory

We provide proofs for the fact that certain orders have no descending chains and no antichains.Comment: Survey pape

Complexity of term representations of finitary functions

The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions, and we show that these bounds are often robust against the change of the basic operations of the structure