In recent years, generalized quantifiers (see [H3]) have received quite a lot of novel interest because of their applications
to computer science and linguistics. Their definability theory has made considerable progress during the last decade, which
will be the subject of the next section. The proofs of many of these results often use results of Ramsey theory, such as theorems
of van derWaerden and Folkman, and yet, the answers to some of the definability problems seem obvious from the outset. This
raises the natural question whether Ramsey theory is really needed in the proofs (cf. [vBW]) or whether easier ways of proof
might be discovered. The purpose of this paper is to argue in favour of the former and to convince the reader of the cruciality
of Ramsey theory for quantifier definability theory.
1991 Mathematics Subject Classification: 03C80, 05D10.