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  1. On the Elementary Theory of Banach Algebras.Angus Macintyre - 1971 - Annals of Pure and Applied Logic 3 (3):239.
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  • A Modal Logic Framework for Reasoning About Comparative Distances and Topology.Mikhail Sheremet, Frank Wolter & Michael Zakharyaschev - 2010 - Annals of Pure and Applied Logic 161 (4):534-559.
    We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic can be (...)
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  • Monadic Theory of Order and Topology in ZFC.Yuri Gurevich & Saharon Shelah - 1982 - Annals of Mathematical Logic 23 (2-3):179-198.
  • The Undecidability of the Lattice of R.E. Closed Subsets of an Effective Topological Space.Sheryl Silibovsky Brady & Jeffrey B. Remmel - 1987 - Annals of Pure and Applied Logic 35 (2):193-203.
    The first-order theory of the lattice of recursively enumerable closed subsets of an effective topological space is proved undecidable using the undecidability of the first-order theory of the lattice of recursively enumerable sets. In particular, the first-order theory of the lattice of recursively enumerable closed subsets of Euclidean n -space, for all n , is undecidable. A more direct proof of the undecidability of the lattice of recursively enumerable closed subsets of Euclidean n -space, n ⩾ 2, is provided using (...)
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  • Free Abelian Lattice-Ordered Groups.A. M. W. Glass, Angus Macintyre & Françoise Point - 2005 - Annals of Pure and Applied Logic 134 (2-3):265-283.
    Let n be a positive integer and FAℓ be the free abelian lattice-ordered group on n generators. We prove that FAℓ and FAℓ do not satisfy the same first-order sentences in the language if m≠n. We also show that is decidable iff n{1,2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices.
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