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  1. A Short Note on the Early History of the Spectrum Problem and Finite Model Theory.Andrea Reichenberger - forthcoming - History and Philosophy of Logic:1-10.
    Finite model theory is currently not one of the hot topics in the philosophy and history of mathematics, not even in the philosophy and history of mathematical logic. The philosophy of mathematics and mathematical logic has concentrated on infinite structures, closely related to foundational issues. In that context, finite models deserved only marginal attention because it was taken for granted that the study of finite structures is trivial compared to the study of infinite structures. In retrospect, research on finite structures (...)
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  • Fifty years of the spectrum problem: survey and new results.Arnaud Durand, Neil D. Jones, Johann A. Makowsky & Malika More - 2012 - Bulletin of Symbolic Logic 18 (4):505-553.
    In 1952, Heinrich Scholz published a question in The Journal of Symbolic Logic asking for a characterization of spectra, i.e., sets of natural numbers that are the cardinalities of finite models of first order sentences. Günter Asser in turn asked whether the complement of a spectrum is always a spectrum. These innocent questions turned out to be seminal for the development of finite model theory and descriptive complexity. In this paper we survey developments over the last 50-odd years pertaining to (...)
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