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Forthcoming articles
  1. Hartry Field (forthcoming). Disarming a Paradox of Validity. Notre Dame Journal of Formal Logic.
    Abstract. Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi (“Two Flavor's of Curry's Paradox”) call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists”. To (...)
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  2.  61
    Hartry Field, Harvey Lederman & Tore Fjetland Øgaard (forthcoming). Prospects for a Naive Theory of Classes. Notre Dame Journal of Formal Logic.
  3.  4
    Bernard Anderson & Barbara Csima (forthcoming). Degrees That Are Not Degrees of Categoricity. Notre Dame Journal of Formal Logic.
    A computable structure $\mathcal {A}$ is $\mathbf {x}$-computably categorical for some Turing degree $\mathbf {x}$ if for every computable structure $\mathcal {B}\cong\mathcal {A}$ there is an isomorphism $f:\mathcal {B}\to\mathcal {A}$ with $f\leq_{T}\mathbf {x}$. A degree $\mathbf {x}$ is a degree of categoricity if there is a computable structure $\mathcal {A}$ such that $\mathcal {A}$ is $\mathbf {x}$-computably categorical, and for all $\mathbf {y}$, if $\mathcal {A}$ is $\mathbf {y}$-computably categorical, then $\mathbf {x}\leq_{T}\mathbf {y}$. We construct a $\Sigma^{0}_{2}$ set whose degree (...)
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  4. M. de Rijke & P. Blackburn (forthcoming). Special Issue on Combining Logics, Volume 37 (2) Of. Notre Dame Journal of Formal Logic.
     
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  5. W. Dean (forthcoming). Algorithms and the Mathematical Foundations of Computer Science. Notre Dame Journal of Formal Logic.
     
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  6. W. Dean (forthcoming). Explicit Modal Logic, Informal Provability and Montague's Paradox. Notre Dame Journal of Formal Logic.
     
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  7.  3
    Jafar S. Eivazloo & Somayyeh Tari (forthcoming). SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures. Notre Dame Journal of Formal Logic.
    Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong CE-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has SCE-cell decomposition if and only if its canonical o-minimal extension has CE-cell decomposition. Then, we show that every weakly o-minimal structure with SCE-cell decomposition satisfies OCP. Our last result implies that every o-minimal structure in which every definable open (...)
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  8.  9
    A. Gareau & R. Padmanabhan (forthcoming). Two Axioms for Implication Algebras. Notre Dame Journal of Formal Logic.
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  9.  3
    Osvaldo Guzmán, Michael Hrušák & Arturo Martínez-Celis (forthcoming). Canjar Filters. Notre Dame Journal of Formal Logic.
    If $\mathcal{F}$ is a filter on $\omega$, we say that $\mathcal{F}$ is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is $F_{\sigma}$, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a $\mathsf{MAD}$ family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the “classical” models (...)
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  10.  4
    Joel David Hamkins & Cole Leahy (forthcoming). Algebraicity and Implicit Definability in Set Theory. Notre Dame Journal of Formal Logic.
    We analyze the effect of replacing several natural uses of definability in set theory by the weaker model-theoretic notion of algebraicity. We find, for example, that the class of hereditarily ordinal algebraic sets is the same as the class of hereditarily ordinal definable sets; that is, $\mathrm{HOA}=\mathrm{HOD}$. Moreover, we show that every algebraic model of $\mathrm{ZF}$ is actually pointwise definable. Finally, we consider the implicitly constructible universe $\mathrm{Imp}$—an algebraic analogue of the constructible universe—which is obtained by iteratively adding not (...)
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  11.  3
    Kristine Harjes & Pavel Naumov (forthcoming). Functional Dependence in Strategic Games. Notre Dame Journal of Formal Logic.
    The article studies properties of functional dependencies between strategies of players in Nash equilibria of multiplayer strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for payoff functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.
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  12.  2
    Horst Herrlich, Paul Howard & Eleftherios Tachtsis (forthcoming). Finiteness Classes and Small Violations of Choice. Notre Dame Journal of Formal Logic.
    We study properties of certain subclasses of the Dedekind finite sets in set theory without the axiom of choice with respect to the comparability of their elements and to the boundedness of such classes, and we answer related open problems from Herrlich’s “The Finite and the Infinite.” The main results are as follows: 1. It is relatively consistent with ZF that the class of all finite sets is not the only finiteness class such that any two of its elements (...)
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  13.  9
    Thomas Hofweber & Ralf Schindler (forthcoming). Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure. Notre Dame Journal of Formal Logic.
    We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated—up to an infinitesimal—by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.
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  14.  4
    Sune Kristian Jakobsen & Jakob Grue Simonsen (forthcoming). Some Remarks on Real Numbers Induced by First-Order Spectra. Notre Dame Journal of Formal Logic.
    The spectrum of a first-order sentence is the set of natural numbers occurring as the cardinalities of finite models of the sentence. In a recent survey, Durand et al. introduce a new class of real numbers, the spectral reals, induced by spectra and pose two open problems associated to this class. In the present note, we answer these open problems as well as other open problems from an earlier, unpublished version of the survey. Specifically, we prove that every algebraic real (...)
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  15. Lars Louder, Chloé Perin & Rizos Sklinos (forthcoming). Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups, to Appear in the Proceedings of the Conference" Recent Developments in Model Theory. Notre Dame Journal of Formal Logic.
     
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  16.  4
    Stephen G. Simpson (forthcoming). Implicit Definability in Arithmetic. Notre Dame Journal of Formal Logic.
    We consider implicit definability over the natural number system $\mathbb{N},+,\times,=$. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of $\mathbb{N}$ which are not explicitly definable from each other. The second theorem says that there exists a subset of $\mathbb{N}$ which is not implicitly definable but belongs to a countable, explicitly definable set of subsets of $\mathbb{N}$. Previous proofs of these theorems have used finite- or infinite-injury priority constructions. (...)
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  17.  2
    Tomoyuki Suzuki (forthcoming). The Distributivity on Bi-Approximation Semantics. Notre Dame Journal of Formal Logic.
    In this paper, we give a possible characterization of the distributivity on bi-approximation semantics. To this end, we introduce new notions of special elements on polarities and show that the distributivity is first-order definable on bi-approximation semantics. In addition, we investigate the dual representation of those structures and compare them with bi-approximation semantics for intuitionistic logic. We also discuss that two different methods to validate the distributivity—by the splitters and by the adjointness—can be explicated with the help of the axiom (...)
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  18. G. Weaver (forthcoming). Dedekind Algebras. Notre Dame Journal of Formal Logic.
     
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