10 found
Order:
  1. An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
  2. A guide to truth predicates in the modern era.Michael Sheard - 1994 - Journal of Symbolic Logic 59 (3):1032-1054.
  3.  47
    Elementary descent recursion and proof theory.Harvey Friedman & Michael Sheard - 1995 - Annals of Pure and Applied Logic 71 (1):1-45.
    We define a class of functions, the descent recursive functions, relative to an arbitrary elementary recursive system of ordinal notations. By means of these functions, we provide a general technique for measuring the proof-theoretic strength of a variety of systems of first-order arithmetic. We characterize the provable well-orderings and provably recursive functions of these systems, and derive various conservation and equiconsistency results.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  4. Weak and strong theories of truth.Michael Sheard - 2001 - Studia Logica 68 (1):89-101.
    A subtheory of the theory of self-referential truth known as FS is shown to be weak as a theory of truth but equivalent to full FS in its proof-theoretic strength.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  5.  40
    The Disjunction and Existence Properties for Axiomatic Systems of Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 40 (1):1--10.
    In a language for arithmetic with a predicate T, intended to mean “ x is the Gödel number of a true sentence”, a set S of axioms and rules of inference has the truth disjunction property if whenever S ⊢ T ∨ T, either S ⊢ T or S ⊢ T. Similarly, S has the truth existence property if whenever S ⊢ ∃χ T ), there is some n such that S ⊢ T ). Continuing previous work, we establish whether (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  6.  57
    The equivalence of the disjunction and existence properties for modal arithmetic.Harvey Friedman & Michael Sheard - 1989 - Journal of Symbolic Logic 54 (4):1456-1459.
    In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  7.  87
    Indecomposable ultrafilters over small large cardinals.Michael Sheard - 1983 - Journal of Symbolic Logic 48 (4):1000-1007.
  8.  30
    Co-critical points of elementary embeddings.Michael Sheard - 1985 - Journal of Symbolic Logic 50 (1):220-226.
    Probably the two most famous examples of elementary embeddings between inner models of set theory are the embeddings of the universe into an inner model given by a measurable cardinal and the embeddings of the constructible universeLinto itself given by 0#. In both of these examples, the “target model” is a subclass of the “ground model”. It is not hard to find examples of embeddings in which the target model is not a subclass of the ground model: ifis a generic (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  9. Truth and Trustworthiness.Michael Sheard - 2015 - In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto, Unifying the Philosophy of Truth. Dordrecht: Imprint: Springer.
     
    Export citation  
     
    Bookmark  
  10.  56
    Anil Gupta and Nuel Belnap. The revision theory of truth. Bradford books. The MIT Press, Cambridge, Mass., and London, 1993, xii + 299 pp. [REVIEW]Michael Sheard - 1995 - Journal of Symbolic Logic 60 (4):1314-1316.