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  1.  27
    Higher dimensional cardinal characteristics for sets of functions.Corey Bacal Switzer - 2022 - Annals of Pure and Applied Logic 173 (1):103031.
  2.  14
    The Cichoń diagram for degrees of relative constructibility.Corey Bacal Switzer - 2020 - Mathematical Logic Quarterly 66 (2):217-234.
    Following a line of research initiated in [4], we describe a general framework for turning reduction concepts of relative computability into diagrams forming an analogy with the Cichoń diagram for cardinal characteristics of the continuum. We show that working from relatively modest assumptions about a notion of reduction, one can construct a robust version of such a diagram. As an application, we define and investigate the Cichoń diagram for degrees of constructibility relative to a fixed inner model W. Many analogies (...)
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  3.  13
    Higher Dimensional Cardinal Characteristics for Sets of Functions II.Jörg Brendle & Corey Bacal Switzer - 2023 - Journal of Symbolic Logic 88 (4):1421-1442.
    We study the values of the higher dimensional cardinal characteristics for sets of functions $f:\omega ^\omega \to \omega ^\omega $ introduced by the second author in [8]. We prove that while the bounding numbers for these cardinals can be strictly less than the continuum, the dominating numbers cannot. We compute the bounding numbers for the higher dimensional relations in many well known models of $\neg \mathsf {CH}$ such as the Cohen, random and Sacks models and, as a byproduct show that, (...)
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  4.  6
    Cohen preservation and independence.Vera Fischer & Corey Bacal Switzer - 2023 - Annals of Pure and Applied Logic 174 (8):103291.
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  5.  3
    Tight Eventually Different Families.Vera Fischer & Corey Bacal Switzer - forthcoming - Journal of Symbolic Logic:1-26.
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  6.  8
    The structure of $$\kappa $$ -maximal cofinitary groups.Vera Fischer & Corey Bacal Switzer - 2023 - Archive for Mathematical Logic 62 (5):641-655.
    We study \(\kappa \) -maximal cofinitary groups for \(\kappa \) regular uncountable, \(\kappa = \kappa ^{. Revisiting earlier work of Kastermans and building upon a recently obtained higher analogue of Bell’s theorem, we show that: Any \(\kappa \) -maximal cofinitary group has \({ many orbits under the natural group action of \(S(\kappa )\) on \(\kappa \). If \(\mathfrak {p}(\kappa ) = 2^\kappa \) then any partition of \(\kappa \) into less than \(\kappa \) many sets can be realized as the (...)
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  7.  3
    Destructibility and axiomatizability of Kaufmann models.Corey Bacal Switzer - 2022 - Archive for Mathematical Logic 61 (7):1091-1111.
    A Kaufmann model is an \(\omega _1\) -like, recursively saturated, rather classless model of \({{\mathsf {P}}}{{\mathsf {A}}}\) (or \({{\mathsf {Z}}}{{\mathsf {F}}} \) ). Such models were constructed by Kaufmann under the combinatorial principle \(\diamondsuit _{\omega _1}\) and Shelah showed they exist in \(\mathsf {ZFC}\) by an absoluteness argument. Kaufmann models are an important witness to the incompactness of \(\omega _1\) similar to Aronszajn trees. In this paper we look at some set theoretic issues related to this motivated by the seemingly (...)
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