Bounds for the Quantifier Depth in Finite-Variable Logics: Alternation Hierarchy. Berkholz, C., Krebs, A., & Verbitsky, O. ACM Trans. Comput. Log. (TOCL), 16(3):21, 2015.
Bounds for the Quantifier Depth in Finite-Variable Logics: Alternation Hierarchy [link]Paper  bibtex   
@article{ dblp1618405,
  title = {Bounds for the Quantifier Depth in Finite-Variable Logics: Alternation Hierarchy},
  author = {Christoph Berkholz and Andreas Krebs and Oleg Verbitsky},
  author_short = {Berkholz, C. and Krebs, A. and Verbitsky, O.},
  bibtype = {article},
  type = {article},
  year = {2015},
  key = {dblp1618405},
  id = {dblp1618405},
  biburl = {http://www.dblp.org/rec/bibtex/journals/tocl/BerkholzKV15},
  url = {http://doi.acm.org/10.1145/2732409},
  journal = {ACM Trans. Comput. Log. (TOCL)},
  pages = {21},
  number = {3},
  volume = {16},
  text = {ACM Trans. Comput. Log. (TOCL) 16(3):21 (2015)}
}

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