Finite-Degree Predicates and Two-Variable First-Order Logic

@inproceedings{Paperman2015FiniteDegreePA,
  title={Finite-Degree Predicates and Two-Variable First-Order Logic},
  author={Charles Paperman},
  booktitle={CSL},
  year={2015}
}
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the order predicate only. From this result we derive the separation of the alternation hierarchy of two-variable logic on this signature. 

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