10 found
  1. A guide to truth predicates in the modern era.Michael Sheard - 1994 - Journal of Symbolic Logic 59 (3):1032-1054.
  2.  35
    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.
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  3.  96
    An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
  4.  98
    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.
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  5.  32
    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.
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  6.  55
    Indecomposable ultrafilters over small large cardinals.Michael Sheard - 1983 - Journal of Symbolic Logic 48 (4):1000-1007.
  7.  26
    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 (...)
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  8. Truth and Trustworthiness.Michael Sheard - 2015 - In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth. Dordrecht: Imprint: Springer.
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    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 (...)
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  10.  30
    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.