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  1. Fixed-Point Extensions of First-Order Logic.Yuri Gurevich & Saharon Shelah - 1986 - Annals of Pure and Applied Logic 32 (3):265-280.
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  • Monadic Generalized Spectra.Ronald Fagin - 1975 - Mathematical Logic Quarterly 21 (1):89-96.
  • Probabilities on Finite Models.Ronald Fagin - 1976 - Journal of Symbolic Logic 41 (1):50-58.
  • Generalized Quantifiers and Pebble Games on Finite Structures.Phokion G. Kolaitis & Jouko A. Väänänen - 1995 - Annals of Pure and Applied Logic 74 (1):23-75.
    First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family (...)
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  • Infinitary Logics and Very Sparse Random Graphs.James F. Lynch - 1997 - Journal of Symbolic Logic 62 (2):609-623.
    Let L ω ∞ω be the infinitary language obtained from the first-order language of graphs by closure under conjunctions and disjunctions of arbitrary sets of formulas, provided only finitely many distinct variables occur among the formulas. Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n) ≪ n -1 satisfies certain simple conditions on its growth rate, then for every σ∈ L ω ∞ω , the probability that σ holds for the (...)
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  • The Hierarchy Theorem for Generalized Quantifiers.Lauri Hella, Kerkko Luosto & Jouko Vaananen - 1996 - Journal of Symbolic Logic 61 (2):802-817.
    The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type $t$ there is a generalized quantifier of type $t$ which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than $t$. This was proved for unary similarity types by Per Lindstrom [17] with (...)
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  • First order predicate logic with generalized quantifiers.Per Lindström - 1966 - Theoria 32 (3):186--195.