Unbounded program memory adds to the expressive power of first-order dynamic logic

The aim of this paper is to-compare various logics of programs with respect to their expressibility. The main result of the paper states that no logic of bounded memory programs is capable of defining the algebra of standard binary trees T = (T, CONS, NIL). Since the usual logics of unbounded memory programs are able to define the above algebra - we derive from the main result a couple of results which solve some questions about comparing expressive powers of programming logics.