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  1. A model-theoretic characterization of the weak pigeonhole principle.Neil Thapen - 2002 - Annals of Pure and Applied Logic 118 (1-2):175-195.
    We bring together some facts about the weak pigeonhole principle from bounded arithmetic, complexity theory, cryptography and abstract model theory. We characterize the models of arithmetic in which WPHP fails as those which are determined by an initial segment and prove a conditional separation result in bounded arithmetic, that PV + lies strictly between PV and S21 in strength, assuming that the cryptosystem RSA is secure.
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  • Divide and Conquer: Dividing Lines and Universality.Saharon Shelah - 2021 - Theoria 87 (2):259-348.
    We discuss dividing lines (in model theory) and some test questions, mainly the universality spectrum. So there is much on conjectures, problems and old results, mainly of the author and also on some recent results.
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  • Relative categoricity in abelian groups II.Wilfrid Hodges & Anatoly Yakovlev - 2009 - Annals of Pure and Applied Logic 158 (3):203-231.
    We consider structures A consisting of an abelian group with a subgroup AP distinguished by a 1-ary relation symbol P, and complete theories T of such structures. Such a theory T is -categorical if T has models A of cardinality λ with AP=κ, and given any two such models A,B with AP=BP, there is an isomorphism from A to B which is the identity on AP. We classify all complete theories of such structures A in terms of the cardinal pairs (...)
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