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  1.  7
    Disjoint Amalgamation in Locally Finite Aec.John T. Baldwin, Martin Koerwien & Michael C. Laskowski - 2017 - Journal of Symbolic Logic 82 (1):98-119.
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  2.  16
    On Absoluteness of Categoricity in Abstract Elementary Classes.Sy-David Friedman & Martin Koerwien - 2011 - Notre Dame Journal of Formal Logic 52 (4):395-402.
    Shelah has shown that $\aleph_1$-categoricity for Abstract Elementary Classes (AECs) is not absolute in the following sense: There is an example $K$ of an AEC (which is actually axiomatizable in the logic $L(Q)$) such that if $2^{\aleph_0}.
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  3.  9
    The Nonabsoluteness of Model Existence in Uncountable Cardinals for $L{Omega{1},Omega}$.Sy-David Friedman, Tapani Hyttinen & Martin Koerwien - 2013 - Notre Dame Journal of Formal Logic 54 (2):137-151.
    For sentences $\phi$ of $L_{\omega_{1},\omega}$, we investigate the question of absoluteness of $\phi$ having models in uncountable cardinalities. We first observe that having a model in $\aleph_{1}$ is an absolute property, but having a model in $\aleph_{2}$ is not as it may depend on the validity of the continuum hypothesis. We then consider the generalized continuum hypothesis context and provide sentences for any $\alpha\in\omega_{1}\setminus\{0,1,\omega\}$ for which the existence of a model in $\aleph_{\alpha}$ is nonabsolute . Finally, we present a complete (...)
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    A Complicated Ω-Stable Depth 2 Theory.Martin Koerwien - 2011 - Journal of Symbolic Logic 76 (1):47 - 65.
    We present a countable complete first order theory T which is model theoretically very well behaved: it eliminates quantifiers, is ω-stable, it has NDOP and is shallow of depth two. On the other hand, there is no countable bound on the Scott heights of its countable models, which implies that the isomorphism relation for countable models is not Borel.
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  5.  5
    Comparing Borel Reducibility and Depth of an Ω-Stable Theory.Martin Koerwien - 2009 - Notre Dame Journal of Formal Logic 50 (4):365-380.
    In "A proof of Vaught's conjecture for ω-stable theories," the notions of ENI-NDOP and eni-depth have been introduced, which are variants of the notions of NDOP and depth known from Shelah's classification theory. First, we show that for an ω-stable first-order complete theory, ENI-NDOP allows tree decompositions of countable models. Then we discuss the relationship between eni-depth and the complexity of the isomorphism relation for countable models of such a theory in terms of Borel reducibility as introduced by Friedman and (...)
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