Ehrenfeucht Games, the Composition Method, and the Monadic Theory of Ordinal Words

@inproceedings{Thomas1997EhrenfeuchtGT,
  title={Ehrenfeucht Games, the Composition Method, and the Monadic Theory of Ordinal Words},
  author={Wolfgang Thomas},
  booktitle={Structures in Logic and Computer Science},
  year={1997}
}
When Ehrenfeucht introduced his game theoretic characterization of elementary equivalence in 1961, the rst application of these \Ehrenfeucht games" was to show that certain ordinals (considered as orderings) are indistinguishable in rst-order logic and weak monadic second-order logic. Here we review Shelah's extension of the method, the \composition of monadic theories", explain it in the example of the monadic theory of the ordinal ordering (!; <), and compare it with the automata theoretic… CONTINUE READING

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