Syntactic Interpretations and Normal Forms

Abstract

In this chapter we collect some results which show to which extent the choice of a symbol set for a mathematical theory is arbitrary. We show, for instance, that the expressive power of first-order languages for group theory does not depend on the choice of S _grp or S _gr as symbol set. The notion of syntactic interpretation will turn out to be a central concept for our considerations. In the section about normal forms we show that, for different syntactic properties, one can find for each formula a logically equivalent one which has this property, e.g., one which has syntactically an especially simple form.