CONTENTS Introduction.................................................................................................................... 5 Section 1. The generalized normal form.................................................................. 9 Section 2. Definability of ordinals by means of the higher operations............... 18 Section 3. Endomorphisms of Ω............................................................................... 28 References.................................................................................................................... 50
[DT] J. Doner and A. Tarski, An extended arithmetic of ordinal numbers, Fund. Math. 65 (1969), pp. 96-127.
[E] A. Ehrenfeucht, Application of games to the completeness problem for formalized theories, Fund. Math. 49 (1961), pp. 129-141.
[F] S. Feferman, Some recent work of Ehrenfeucht and Fraissé, Summaries of talks presented at the Summer Institute for Symbolic Logic, Cornell University, 1957. Second Edition, Princeton, New Jersey 1960.
[FR] R. Fraissé, Sur quelques classifications des relations basées sur des isomorphismes restrainies, Publications Scientifiques de l'Universite d'Alger, Série A (mathématiques), 2 (1955), pp. 15-60 and pp. 273-295.
[MT] A. Mostowski and A. Tarski, Arithmetically definable classes and types of well-ordered systems, Bull. Amer. Math. Soc. 55 (1949), p. 65, Abstract 55-1-78; erratum ibid., p. 1192.
[T] A. Tarski, Contributions to the theory of models: I, Indag. Math. 16 (1954), pp. 572-581; II, ibid. 16 (1954), pp. 582-588; III, ibid. 17 (1955), pp. 56-64.
[TV] A. Tarski and R. L. Vaught, Arithmetical extensions of relational systems, Compositio Math. 13 (1957), pp. 81-102.