@inproceedings{KRB08stacs,
  abstract = "We investigate structures that can be represented by omega-automata, so called omega-automatic structures, and prove that relations defined over such structures in first-order logic expanded by the first-order quantifiers `there exist at most $\aleph_0$ many', 'there exist finitely many' and 'there exist $k$ modulo $m$ many' are omega-regular. The proof identifies certain algebraic properties of omega-semigroups. As a consequence an omega-regular equivalence relation of countable index has an omega-regular set of representatives. This implies Blumensath's conjecture that a countable structure with an $\omega$-automatic presentation can be represented using automata on finite words. This also complements a very recent result of Hj�rth, Khoussainov, Montalban and Nies showing that there is an omega-automatic structure which has no injective presentation.",
  author = "Lukasz Kaiser and Sasha Rubin and Vince Barany",
  booktitle = "Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008",
  editor = "S. Albers and P. Weil",
  pages = "385-396",
  title = "Cardinality and counting quantifiers on omega-automatic structures",
  url = "http://hal.archives-ouvertes.fr/hal-00227560/",
  year = "2008",
}