REHMTJ Note added September 1, 1986. In a remarkable last-minute ____ _____ _________ __ ____contribution to this volume, Friedman, Robertson and Seymour have shownthat the Robertson-Seymour Theorem 4.6 (well quasiorderedness of finitegraphs under minor embeddability) finitistically implies Friedman'sTheorem 4.7 (well quasiorderedness of finite labeled trees under gapembeddability). It follows that the Robertson-Seymour Theorem, as well asfinite miniaturizations of it, are not provable in the strong system 1P -CA . Thus the suspicions which were expressed above in connection with 1 0Theorems 4.6 and 4.7 are fully vindicated.