Monadic Theory of a Linear Order Versus the Theory of its Subsets with the Lifted Min/Max Operations
نویسندگان
چکیده
We compare the monadic second-order theory of an arbitrary linear ordering L with the theory of the family of subsets of L endowed with the operation on subsets obtained by lifting the max operation on L. We show that the two theories define the same relations. The same result holds when lifting the min operation or both max and min operations.
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The first-order theory of linear order is far from trivia!. The monadic (secondorder) theory of linear order is much stronger. Stil~ surpr,Mng decidability results were proven in that direction. Rabin proved in [10i that the monadic theory of the rational chain is decidable. Hence the monadic theory of all countable linear orders is decidable. Biichi proved in [I] that the monadic theory of ord...
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