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  1.  11
    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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  2.  29
    A Guide to Truth Predicates in the Modern Era.Michael Sheard - 1994 - Journal of Symbolic Logic 59 (3):1032-1054.
  3.  43
    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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  4.  13
    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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  5.  20
    Indecomposable Ultrafilters Over Small Large Cardinals.Michael Sheard - 1983 - Journal of Symbolic Logic 48 (4):1000-1007.
  6.  7
    Gupta Anil and Belnap Nuel. 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.
  7.  16
    Co-Critical Points of Elementary Embeddings.Michael Sheard - 1985 - Journal of Symbolic Logic 50 (1):220-226.
  8.  5
    Review: Anil Gupta, Nuel Belnap, The Revision Theory of Truth. [REVIEW]Michael Sheard - 1995 - Journal of Symbolic Logic 60 (4):1314-1316.
  9. Truth and Trustworthiness.Michael Sheard - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag.
     
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  10.  36
    An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
  11.  11
    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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