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  1. Bounded Scott Set Saturation.Alex M. McAllister - 2002 - Mathematical Logic Quarterly 48 (2):245-259.
    We examine the relationship between two different notions of a structure being Scott set saturated and identify sufficient conditions which guarantee that a structure is uniquely Scott set saturated. We also consider theories representing Scott sets; in particular, we identify a sufficient condition on a theory T so that for any given countable Scott set there exists a completion of T that is saturated with respect to the given Scott set. These results extend Scott's characterization of countable Scott sets via (...)
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  • A standard model of Peano Arithmetic with no conservative elementary extension.Ali Enayat - 2008 - Annals of Pure and Applied Logic 156 (2):308-318.
    The principal result of this paper answers a long-standing question in the model theory of arithmetic [R. Kossak, J. Schmerl, The Structure of Models of Peano Arithmetic, Oxford University Press, 2006, Question 7] by showing that there exists an uncountable arithmetically closed family of subsets of the set ω of natural numbers such that the expansion of the standard model of Peano arithmetic has no conservative elementary extension, i.e., for any elementary extension of , there is a subset of ω* (...)
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  • Representing Scott sets in algebraic settings.Alf Dolich, Julia F. Knight, Karen Lange & David Marker - 2015 - Archive for Mathematical Logic 54 (5-6):631-637.
    We prove that for every Scott set S there are S-saturated real closed fields and S-saturated models of Presburger arithmetic.
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  • The Borel Complexity of Isomorphism for Theories with Many Types.David Marker - 2007 - Notre Dame Journal of Formal Logic 48 (1):93-97.
    During the Notre Dame workshop on Vaught's Conjecture, Hjorth and Kechris asked which Borel equivalence relations can arise as the isomorphism relation for countable models of a first-order theory. In particular, they asked if the isomorphism relation can be essentially countable but not tame. We show this is not possible if the theory has uncountably many types.
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  • Which set existence axioms are needed to prove the separable Hahn-Banach theorem?Douglas K. Brown & Stephen G. Simpson - 1986 - Annals of Pure and Applied Logic 31:123-144.
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