Axioms for abstract model theory

Annals of Mathematical Logic 7 (2-3):221-265 (1974)
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Logical Indefinites.Jack Woods - 2014 - Logique Et Analyse -- Special Issue Edited by Julien Murzi and Massimiliano Carrara 227: 277-307.
Definability hierarchies of general quantifiers.Lauri Hella - 1989 - Annals of Pure and Applied Logic 43 (3):235.
Logicality and model classes.Juliette Kennedy & Jouko Väänänen - 2021 - Bulletin of Symbolic Logic 27 (4):385-414.

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References found in this work

Infinitary logic and admissible sets.Jon Barwise - 1969 - Journal of Symbolic Logic 34 (2):226-252.
Absolute logics and L∞ω.K. Jon Barwise - 1972 - Annals of Mathematical Logic 4 (3):309-340.
Hanf Numbers for Fragments of L ∞ω.Jon Barwise & Kenneth Kunen - 1984 - Journal of Symbolic Logic 49 (1):315-315.

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