Year:

  1.  13
    A Note on FDE “All the Way Up”.Jc Beall & Caleb Camrud - 2020 - Notre Dame Journal of Formal Logic 61 (2):283-296.
    A very natural and philosophically important subclassical logic is FDE. This account of logical consequence can be seen as going beyond the standard two-valued account to a four-valued account. A natural question arises: What account of logical consequence arises from considering further combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different context. In this note we generalize Priest’s result to show (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  2.  1
    Isometry Groups of Borel Randomizations.Alexander Berenstein & Rafael Zamora - 2020 - Notre Dame Journal of Formal Logic 61 (2):297-316.
    We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. We show that if properties such as the Rokhlin property, topometric generics, and extreme amenability hold for the isometry group of the structure, then they also hold in the isometry group of the randomization.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  3.  10
    The Formalities of Temporaryism Without Presentness.Fabrice Correia & Sven Rosenkranz - 2020 - Notre Dame Journal of Formal Logic 61 (2):181-202.
    Temporaryism—the view that not always everything always exists—comes in two main versions: presentism and expansionism. Both versions of the view are commonly formulated using the notion of being present, which we, among others, find problematic. Expansionism is also sometimes accused of requiring extraordinary conceptual tools for its formulation. In this paper, we put forward systematic characterizations of presentism and expansionism which involve neither the notion of being present nor unfamiliar conceptual tools. These characterizations are full-blown logics, each logic comprising an (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4.  2
    Distality for the Asymptotic Couple of the Field of Logarithmic Transseries.Allen Gehret & Elliot Kaplan - 2020 - Notre Dame Journal of Formal Logic 61 (2):341-361.
    We show that the theory Tlog of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP, this provides a new proof that Tlog is NIP.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  14
    Formal Notes on the Substitutional Analysis of Logical Consequence.Volker Halbach - 2020 - Notre Dame Journal of Formal Logic 61 (2):317-339.
    Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  6.  4
    Uniformly Bounded Arrays and Mutually Algebraic Structures.Michael C. Laskowski & Caroline A. Terry - 2020 - Notre Dame Journal of Formal Logic 61 (2):265-282.
    We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure M. We prove that if T is a complete L-theory, then T is mutually algebraic if and only if there is some model M of T for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory T is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model M of T.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  7.  1
    Effective Domination and the Bounded Jump.Keng Meng Ng & Hongyuan Yu - 2020 - Notre Dame Journal of Formal Logic 61 (2):203-225.
    We study the relationship between effective domination properties and the bounded jump. We answer two open questions about the bounded jump: We prove that the analogue of Sacks jump inversion fails for the bounded jump and the wtt-reducibility. We prove that no c.e. bounded high set can be low by showing that they all have to be Turing complete. We characterize the class of c.e. bounded high sets as being those sets computing the Halting problem via a reduction with use (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  8.  2
    A Note on Strongly Almost Disjoint Families.Guozhen Shen - 2020 - Notre Dame Journal of Formal Logic 61 (2):227-231.
    For a set M, let |M| denote the cardinality of M. A family F is called strongly almost disjoint if there is an n∈ω such that |A∩B|<n for any two distinct elements A, B of F. It is shown in ZF (without the axiom of choice) that, for all infinite sets M and all strongly almost disjoint families F⊆P(M), |F|<|P(M)| and there are no finite-to-one functions from P(M) into F, where P(M) denotes the power set of M.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9. On Amalgamation in NTP $_{2}$ Theories and Generically Simple Generics.Pierre Simon - 2020 - Notre Dame Journal of Formal Logic 61 (2):233-243.
    We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP2 theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  10.  2
    An Effective Analysis of the Denjoy Rank.Linda Westrick - 2020 - Notre Dame Journal of Formal Logic 61 (2):245-263.
    We analyze the descriptive complexity of several Π11-ranks from classical analysis which are associated to Denjoy integration. We show that VBG, VBG∗, ACG, and ACG∗ are Π11-complete, answering a question of Walsh in case of ACG∗. Furthermore, we identify the precise descriptive complexity of the set of functions obtainable with at most α steps of the transfinite process of Denjoy totalization: if |⋅| is the Π11-rank naturally associated to VBG, VBG∗, or ACG∗, and if α<ωck1, then {F∈C(I):|F|≤α} is Σ02α-complete. These (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11.  2
    A Lindström Theorem for Intuitionistic Propositional Logic.Guillermo Badia - 2020 - Notre Dame Journal of Formal Logic 61 (1):11-30.
    We show that propositional intuitionistic logic is the maximal abstract logic satisfying a certain form of compactness, the Tarski union property, and preservation under asimulations.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  12.  5
    Questions and Dependency in Intuitionistic Logic.Ivano Ciardelli, Rosalie Iemhoff & Fan Yang - 2020 - Notre Dame Journal of Formal Logic 61 (1):75-115.
    In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, where teams are embedded within intuitionistic Kripke models. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13.  6
    Short Proofs for Slow Consistency.Anton Freund & Fedor Pakhomov - 2020 - Notre Dame Journal of Formal Logic 61 (1):31-49.
    Let Con↾x denote the finite consistency statement “there are no proofs of contradiction in T with ≤x symbols.” For a large class of natural theories T, Pudlák has shown that the lengths of the shortest proofs of Con↾n in the theory T itself are bounded by a polynomial in n. At the same time he conjectures that T does not have polynomial proofs of the finite consistency statements Con)↾n. In contrast, we show that Peano arithmetic has polynomial proofs of Con)↾n, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14.  5
    The Logic of Turing Progressions.Eduardo Hermo Reyes & Joost J. Joosten - 2020 - Notre Dame Journal of Formal Logic 61 (1):155-180.
    Turing progressions arise by iteratedly adding consistency statements to a base theory. Different notions of consistency give rise to different Turing progressions. In this paper we present a logic that generates exactly all relations that hold between these different Turing progressions given a particular set of natural consistency notions. Thus, the presented logic is proven to be arithmetically sound and complete for a natural interpretation, named the formalized Turing progressions interpretation.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  15. Canonization of Smooth Equivalence Relations on Infinite-Dimensional $Mathsf{E}_{0}$-Large Products.Vladimir Kanovei & Vassily Lyubetsky - 2020 - Notre Dame Journal of Formal Logic 61 (1):117-128.
    We propose a canonization scheme for smooth equivalence relations on Rω modulo restriction to E0-large infinite products. It shows that, given a pair of Borel smooth equivalence relations E, F on Rω, there is an infinite E0-large perfect product P⊆Rω such that either F⊆E on P, or, for some ℓ<ω, the following is true for all x,y∈P: xEy implies x=y, and x↾=y↾ implies xFy.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  16.  10
    A Remark on Probabilistic Measures of Coherence.Sergi Oms - 2020 - Notre Dame Journal of Formal Logic 61 (1):129-140.
    In recent years, some authors have proposed quantitative measures of the coherence of sets of propositions. Such probabilistic measures of coherence are, in general terms, functions that take as their argument a set of propositions and yield as their value a number that is supposed to represent the degree of coherence of the set. In this paper, I introduce a minimal constraint on PMC theories, the weak stability principle, and show that any correct, coherent, and complete PMC cannot satisfy it. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  17.  5
    Splittings and Disjunctions in Reverse Mathematics.Sam Sanders - 2020 - Notre Dame Journal of Formal Logic 61 (1):51-74.
    Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with two RM-phenomena, namely, splittings and disjunctions. As to splittings, there are some examples in RM of theorems A, B, C such that A↔, that is, A can be split into two (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  18.  2
    Pseudofiniteness in Hrushovski Constructions.Ali N. Valizadeh & Massoud Pourmahdian - 2020 - Notre Dame Journal of Formal Logic 61 (1):1-10.
    In a relational language consisting of a single relation R, we investigate pseudofiniteness of certain Hrushovski constructions obtained via predimension functions. It is notable that the arity of the relation R plays a crucial role in this context. When R is ternary, by extending the methods recently developed by Brody and Laskowski, we interpret 〈Q+,<〉 in the 〈K+,≤∗〉-generic and prove that this structure is not pseudofinite. This provides a negative answer to the question posed in an earlier work by Evans (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  19.  1
    The Complexity of Radicals and Socles of Modules.Huishan Wu - 2020 - Notre Dame Journal of Formal Logic 61 (1):141-153.
    This paper studies two dual notions in module theory—namely, radicals and socles—from the standpoint of reverse mathematics. We first consider radicals of Z-modules, where the radical of a Z-module M is defined as the intersection of pM={px:x∈M} with p taken from all primes. It shows that ACA0 is equivalent to the existence of radicals of Z-modules over RCA0. We then study socles of modules over commutative rings with identity. The socle of an R-module M is the largest semisimple submodule of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
 Previous issues
  
Next issues