Abstract
We apply the method of model theoretic games to theories of linear order. We obtain the known “equivalence” between ω -regular sets and the monadic second-order theory of ( ω , <) and the known “equivalence” between the star free regular sets and the first-order theory of finite linear orders. Finally, we give a new decision procedure for the monadic second order theory of ( ω , <) which does not rely on a reduction to the emptiness problem for automata on ω -words.
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