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  1.  7
    Beyond Berkson: Further Light on the Selection Bias.David Atkinson & Jeanne Peijnenburg - 2025 - Notre Dame Journal of Formal Logic 66 (1):143-152.
    The Berkson effect shows that two independent diseases, A and B, become negatively correlated if they are confined within the walls of a hospital. We explain that, simply by adding a third disease, C, the negative correlation may flip into a positive one, and we identify the point where this happens. That leads to a necessary and sufficient condition for a positive as well as a negative correlation between A and B. We further explain that a flip from negative to (...)
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  2.  9
    Completeness of Infinitary Heterogeneous Logic.Christian Espíndola - 2025 - Notre Dame Journal of Formal Logic 66 (1):1-17.
    Given a regular cardinal κ such that κ<κ=κ (e.g., if the generalized continuum hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite alternating sequences of quantifiers) within the language Lκ+,κ, where there are conjunctions and disjunctions of at most κ many formulas and quantification (including the heterogeneous one) is applied to less than κ many variables. This type of quantification is interpreted in Set using the usual second-order formulation in terms of strategies (...)
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  3.  7
    Planar Graphs with Separation Are dp-Minimal.Javier de la Nuez González - 2025 - Notre Dame Journal of Formal Logic 66 (1):57-78.
    We prove that, given a planar embedding of a graph in the sphere, the expansion of the graph structure by predicates encoding vertex separation by simple graph cycles is dp-minimal. This provides a rich natural class of examples of unstable, dp-minimal, and also monadically NIP theories. We also show how to infer the existence of a distal expansion of the theory of the Farey graph.
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  4. The Marker–Steinhorn Theorem.Pablo Andújar Guerrero - 2025 - Notre Dame Journal of Formal Logic 66 (1):1-10.
    We give a proof of the Marker–Steinhorn theorem which fills a gap in previous proofs of the result.
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  5.  10
    Broad Infinity and Generation Principles.Paul Blain Levy - 2025 - Notre Dame Journal of Formal Logic 66 (1):79-141.
    We introduce Broad Infinity, a new set-theoretic axiom scheme based on the slogan “Every time we construct a new element, we gain a new arity.” It says that three-dimensional trees whose growth is controlled by a specified class function form a set. Such trees are called broad numbers. Assuming AC (the axiom of choice) or at least the weak version known as WISC (weakly initial set of covers), we show that Broad Infinity is equivalent to Mahlo’s principle, which says that (...)
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  6.  18
    Core Tarski and Core McGee.Neil Tennant - 2025 - Notre Dame Journal of Formal Logic 66 (1):1-25.
    We furnish a core-logical development of the Gödel numbering framework that allows metamathematicians to attain limitative results about arithmetical truth without incorporating a genuine truth predicate into the language in a way that would lead to semantic closure. We show how Tarski’s celebrated theorem on the arithmetical undefinability of arithmetical truth can be established using only core logic in both the object language and the metalanguage. We do so at a high level of abstraction, by augmenting the usual first-order language (...)
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  7.  3
    Provable Better-Quasi-Orders.Anton Freund, Alberto Marcone, Fedor Pakhomov & Giovanni Soldà - 2025 - Notre Dame Journal of Formal Logic -1:1-14.
    It has recently been shown that fairly strong axiom systems such as ACA0 cannot prove that the antichain with three elements is a better-quasi-order (bqo). In the present paper, we give a complete characterization of the finite partial orders that are provably bqo in such axiom systems. The result will also be extended to infinite orders. As an application, we derive that a version of the minimal bad array lemma is weak over ACA0. In sharp contrast, a recent result shows (...)
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  8. Iterating Both and Neither: With Applications to the Paradoxes.Levin Hornischer - 2025 - Notre Dame Journal of Formal Logic -1:1-43.
    A common response to the paradoxes of vagueness and truth is to introduce the truth-values “neither true nor false” or “both true and false” (or both). However, this infamously runs into trouble with higher-order vagueness or the revenge paradox. This, and other considerations, suggest iterating “both” and “neither”: as in “neither true nor neither true nor false.” We present a novel explication of iterating “both” and “neither.” Unlike previous approaches, each iteration will change the logic, and the logic in the (...)
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  9.  3
    Stabilizers, Measures, and IP Sets.Amador Martin-Pizarro & Daniel Palacín - 2025 - Notre Dame Journal of Formal Logic -1.
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  10.  2
    Orthogonal Definable Subspaces of Hilbert Spaces: An Application of Goldblatt’s Method.Shengyang Zhong - 2025 - Notre Dame Journal of Formal Logic -1.
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