Trees and Ehrenfeucht–Fraı̈ssé games Original Research Article

Trees are natural generalizations of ordinals and this is especially apparent when one tries to find an uncountable analogue of the concept of the Scott-rank of a countable structure. The purpose of this paper is to introduce new methods in the study of an ordering between trees whose analogue is the usual ordering between ordinals. For example, one of the methods is the tree-analogue of the successor operation on the ordinals. ☆ This paper is based on notes taken by the second author of lectures given by the first author in the University of Helsinki in the fall term of 1993. Corresponding author contact information Corresponding author 3 Partially supported by grants from SFS and NSERC. 2 Partially supported by grant 1011049 of the Academy of Finland. Part of this paper was prepared during December 1995–January 1996, while the second author visited the DIMACS center in New Jersey.