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  Over Words, Two Variables Are as Powerful as One Quantifier Alternation: FO 2

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by Sigma \pi, Thomas Wilke
http://www.cs.mcgill.ca/~denis/papers/stoc98.ps
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Abstract:

Abstract. We show a property of strings is expressible in the twovariable fragment of first-order logic if and only if it is expressible by both a \Sigma 2 and a \Pi 2 sentence. We thereby establish: UTL = FO

Citations

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