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  1. Metric abstract elementary classes as accessible categories.M. Lieberman & J. Rosický - 2017 - Journal of Symbolic Logic 82 (3):1022-1040.
    We show that metric abstract elementary classes are, in the sense of [15], coherent accessible categories with directed colimits, with concrete ℵ1-directed colimits and concrete monomorphisms. More broadly, we define a notion of κ-concrete AEC—an AEC-like category in which only the κ-directed colimits need be concrete—and develop the theory of such categories, beginning with a category-theoretic analogue of Shelah’s Presentation Theorem and a proof of the existence of an Ehrenfeucht–Mostowski functor in case the category is large. For mAECs in particular, (...)
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  • Model theory of a Hilbert space expanded with an unbounded closed selfadjoint operator.Camilo Enrique Argoty Pulido - 2014 - Mathematical Logic Quarterly 60 (6):403-424.
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  • Tameness in generalized metric structures.Michael Lieberman, Jiří Rosický & Pedro Zambrano - 2023 - Archive for Mathematical Logic 62 (3):531-558.
    We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a proof of concept we show that the result of Boney and Zambrano (Around the set-theoretical consistency of d-tameness of metric abstract elementary classes, arXiv:1508.05529, 2015) on (metric) tameness under a large cardinal assumption holds in this more general context. We briefly consider a further generalization to partial metric spaces, and hint at connections (...)
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  • The kim–pillay theorem for abstract elementary categories.Mark Kamsma - 2020 - Journal of Symbolic Logic 85 (4):1717-1741.
    We introduce the framework of AECats, generalizing both the category of models of some first-order theory and the category of subsets of models. Any AEC and any compact abstract theory forms an AECat. In particular, we find applications in positive logic and continuous logic: the category of models of a positive or continuous theory is an AECat. The Kim–Pillay theorem for first-order logic characterizes simple theories by the properties dividing independence has. We prove a version of the Kim–Pillay theorem for (...)
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  • Reduction of database independence to dividing in atomless Boolean algebras.Tapani Hyttinen & Gianluca Paolini - 2016 - Archive for Mathematical Logic 55 (3-4):505-518.
    We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections between independence in database theory and stochastic independence. As indeed, in light of the aforementioned reduction and recent work of Ben-Yaacov :957–1012, 2013), the former case of independence can be seen as the discrete version of the latter.
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  • Tameness from large cardinal axioms.Will Boney - 2014 - Journal of Symbolic Logic 79 (4):1092-1119.
    We show that Shelah’s Eventual Categoricity Conjecture for successors follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC withLS below a strongly compact cardinalκis <κ-tame and applying the categoricity transfer of Grossberg and VanDieren [11]. These techniques also apply to measurable and weakly compact cardinals and we prove similar tameness results under those hypotheses. We isolate a dual property (...)
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  • A presentation theorem for continuous logic and metric abstract elementary classes.Will Boney - 2017 - Mathematical Logic Quarterly 63 (5):397-414.
    In recent years, model theory has widened its scope to include metric structures by considering real-valued models whose underlying set is a complete metric space. We show that it is possible to carry out this work by giving presentation theorems that translate the two main frameworks into discrete settings. We also translate various notions of classification theory.
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  • 2010 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '10.Uri Abraham & Ted Slaman - 2011 - Bulletin of Symbolic Logic 17 (2):272-329.
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