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Creators/Authors contains: "Laskowski, Michael"

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  1. ; (, Bulletin of the London Mathematical Society)
    Abstract We prove various results around indiscernibles in monadically NIP theories. First, we provide several characterizations of monadic NIP in terms of indiscernibles, mirroring previous characterizations in terms of the behavior of finite satisfiability. Second, we study (monadic) distality in hereditary classes and complete theories. Here, via finite combinatorics, we prove a result implying that every planar graph admits a distal expansion. Finally, we prove a result implying that no monadically NIP theory interprets an infinite group, and note an example of a (monadically) stable theory with no distal expansion that does not interpret an infinite group. 
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    Free, publicly-accessible full text available July 25, 2026
  2. ; (, Transactions of the American Mathematical Society, Series B)
    The authors correct results in “Characterizations of monadic NIP” [Trans. Amer. Math. Soc. Ser. B 8 (2021), pp. 948–970]. The notion of endless indiscernible triviality is introduced and replaces indiscernible triviality throughout, in particular in Theorem 1.1. The claim regarding the failure of 4-wqo in Theorem 1.2 is withdrawn and remains unproved. 
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  3. ; ; (, Model Theory)
    For an $$\aleph_1$$-categorical atomic class, we clarify the space of types over the unique model of size $$\aleph_1$$. Using these results, we prove that if such a class has a model of size $$\beth_1^+$$ then it is $$\omega$$-stable. 
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  4. ; (, The Journal of Symbolic Logic)
    Abstract We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete one-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $$M^{eq}$$ has a Borel complete reduct, and if a theory T is not $$\omega $$ -stable, then the elementary diagram of some countable model of T has a Borel complete reduct. 
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  5. ; (, Fundamenta Mathematicae)
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  6. ; (, Proceedings of the American Mathematical Society)
    We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a theory T T is mutually algebraic if and only if there is a uniform bound on the number of coordinate-wise non-algebraic types over every model, regardless of its cardinality. 
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  7. ; (, The Journal of Symbolic Logic)
    Abstract We show that if a countable structure M in a finite relational language is not cellular, then there is an age-preserving $$N \supseteq M$$ such that $$2^{\aleph _0}$$ many structures are bi-embeddable with N . The proof proceeds by a case division based on mutual algebraicity. 
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  8. ; (, Archive for Mathematical Logic)
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  9. ; (, Model Theory)
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  10. ; (, Transactions of the American Mathematical Society, Series B)
    We give several characterizations of when a complete first-order theory T T is monadically NIP, i.e. when expansions of T T by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers. 
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