Ehrenfeucht games, the composition method, and the monadic theory of ordinal words

Abstract

When Ehrenfeucht introduced his game theoretic characterization ofelementary equivalence in 1961, the first application of theseEhrenfeuchtgamesEhrenfeucht gameswas to show that certain ordinals (consideredas orderings) are indistinguishable in first-order logic and weakmonadic second-order logic. Here we review Shelah's extension ofthe method, thewas to show that certain ordinals (considered as orderings)are indistinguishable in first-order logic and weak monadic second-orderlogic. Here we review Shelah's extension of the method, thecompositionof monadic theoriescomposition of monadic theories, explain it inthe example of the monadic theory of the ordinal ordering (, explainit in the example of the monadic theory of the ordinal ordering (,