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Fragments of First-Order Logic over Infinite Words Diekert, Volker Kufleitner, Manfred Infinite words Regular languages First-order logic Automata theory Semigroups Topology We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic $\mathrm{FO}[<]$ for $\omega$-languages: $\Sigma_2$, $\Delta_2$, $\mathrm{FO}^2 \cap \Sigma_2$ (and by duality $\mathrm{FO}^2 \cap \Pi_2$), and $\mathrm{FO}^2$. These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke (1998) and Boja{\'n}czyk (2008) and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Volker Diekert and Manfred Kufleitner 2009 Is Part Of LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2009.1818 urn:nbn:de:0030-drops-18185 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1818 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode