Large Finite Sets

The more complicated notation we have for K t,he more complicated will the a-large sets be. KETOSEN developed his theory in RETONEN and SOLOVAY [3]. The theory there was used to give a generalization of RAMSEY’S theorem. They gave a combinatorial proof of the Paris-Harrington result (PARIS and HARRINGTON [S]). The a-large sets were used to give bounds in the following direction : any generalized Ramsey-function grows less fast than some n-recursive function where a < c 0 .