This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Siblings:
19 found
Search inside:
(import / add options)   Sort by:
  1. Andrew Arana (2004). Arithmetical Independence Results Using Higher Recursion Theory. Journal of Symbolic Logic 69 (1):1-8.
    We extend an independence result proved in our earlier paper "Solovay's Theorem Cannot Be Simplified" (Annals of Pure and Applied Logic 112 (2001)). Our method uses the Barwise.
    Remove from this list | Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  2. Justin Clarke-Doane (2013). What is Absolute Undecidability?†. Noûs 47 (3):467-481.
    It is often alleged that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical (...)
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  3. Melvin Fitting (1972). Non-Classical Logics and the Independence Results of Set Theory. Theoria 38 (3):133-142.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  4. T. E. Forster (1983). Further Consistency and Independence Results in NF Obtained by the Permutation Method. Journal of Symbolic Logic 48 (2):236-238.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  5. Harvey Friedman, Discrete Independence Results.
    A bi-infinite approximate fixed point of type (n,k) is an approximate fixed point of type (n,k) whose terms are biinfinite; i.e., contain infin-itely many positive and infinitely many negative elements.
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  6. Harvey Friedman, New Borel Independence Results.
    S. Adams, W. Ambrose, A. Andretta, H. Becker, R. Camerlo, C. Champetier, J.P.R. Christensen, D.E. Cohen, A. Connes. C. Dellacherie, R. Dougherty, R.H. Farrell, F. Feldman, A. Furman, D. Gaboriau, S. Gao, V. Ya. Golodets, P. Hahn, P. de la Harpe, G. Hjorth, S. Jackson, S. Kahane, A.S. Kechris, A. Louveau,, R. Lyons, P.-A. Meyer, C.C. Moore, M.G. Nadkarni, C. Nebbia, A.L.T. Patterson, U. Krengel, A.J. Kuntz, J.-P. Serre, S.D. Sinel'shchikov, T. Slaman, Solecki, R. Spatzier, J. Steel, D. Sullivan, S. (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  7. Harvey Friedman (2003). Primitive Independence Results. Journal of Mathematical Logic 3 (01):67-83.
    We present some new set and class theoretic independence results from ZFC and NBGC that are particularly simple and close to the primitives of membership and equality (see sections 4,5). They are shown to be equivalent to familiar small large cardinal hypotheses. We modify these independendent statements in order to give an example of a sentence in set theory with 5 quantifiers which is independent of ZFC (see section 6). It is known that all 3 quantifier sentences are decided in (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  8. Paul E. Howard, Arthur L. Rubin & Jean E. Rubin (1978). Independence Results for Class Forms of the Axiom of Choice. Journal of Symbolic Logic 43 (4):673-684.
    Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  9. Sanjay Jain & Jochen Nessel (2001). Some Independence Results for Control Structures in Complete Numberings. Journal of Symbolic Logic 66 (1):357-382.
    Acceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  10. Renling Jin (1991). Some Independence Results Related to the Kurepa Tree. Notre Dame Journal of Formal Logic 32 (3):448-457.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  11. Juliette Kennedy & Roman Kossak (eds.) (2012). Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies. Cambridge University Press.
    Machine generated contents note: 1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture W. Hugh Woodin; 4. [omega]-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts James H. (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  12. Jan Krajíček (1997). Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. Journal of Symbolic Logic 62 (2):457-486.
    A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: (1) Feasible (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  13. Michael E. Levin & Margarita R. Levin (1978). The Independence Results of Set Theory: An Informal Exposition. Synthese 38 (1):1 - 34.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  14. Patricia Marino (2006). John L. BELL. Set Theory: Boolean-Valued Models and Independence Proofs. Oxford: Clarendon Press, 2005. Oxford Logic Guides, No. 47. Pp. XXII + 191. ISBN 0-19-856852-5, 987-0-19-856852-0 (Pbk). [REVIEW] Philosophia Mathematica 14 (3):392-394.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  15. J. B. Paris (1978). Some Independence Results for Peano Arithmetic. Journal of Symbolic Logic 43 (4):725-731.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  16. Richard Pettigrew (2010). The Foundations of Arithmetic in Finite Bounded Zermelo Set Theory. Cahiers du Centre de Logique 17:99-118.
    In this paper, I pursue such a logical foundation for arithmetic in a variant of Zermelo set theory that has axioms of subset separation only for quantifier-free formulae, and according to which all sets are Dedekind finite. In section 2, I describe this variant theory, which I call ZFin0. And in section 3, I sketch foundations for arithmetic in ZFin0 and prove that certain foundational propositions that are theorems of the standard Zermelian foundation for arithmetic are independent of ZFin0.<br><br>An equivalent (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  17. Saharon Shelah (1980). Independence Results. Journal of Symbolic Logic 45 (3):563-573.
    We prove independence results concerning the number of nonisomorphic models (using the S-chain condition and S-properness) and the consistency of "ZCF + 2 ℵ 0 = ℵ 2 + there is a universal linear order of power ℵ 1 ". Most of these results were announced in [Sh 4], [Sh 5]. In subsequent papers we shall prove an analog f MA for forcing which does not destroy stationary subsets of ω 1 , investigate D-properness for various filters and prove the (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  18. Vítězslav Švejdar (1991). Some Independence Results in Interpretability Logic. Studia Logica 50 (1):29 - 38.
    A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  19. Krzysztof Wójtowicz (2006). Independence and Justification in Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373.
    In the article the problem of independence in mathematics is discussed. The status of the continuum hypothesis, large cardinal axioms and the axiom of constructablility is presented in some detail. The problem whether incompleteness is really relevant for ordinary mathematics and for empirical science is investigated. Another aim of the article is to give some arguments for the thesis that the problem of reliability and justification of new axioms is well-posed and worthy of attention. In my opinion, investigations concerning the (...)
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation