9 found
  1.  2
    Harvey Friedman & Michael Sheard (1995). Elementary Descent Recursion and Proof Theory. 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.  20
    Michael Sheard (1994). A Guide to Truth Predicates in the Modern Era. Journal of Symbolic Logic 59 (3):1032-1054.
  3.  30
    Michael Sheard (2001). Weak and Strong Theories of Truth. 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.  11
    Harvey Friedman & Michael Sheard (1989). The Equivalence of the Disjunction and Existence Properties for Modal Arithmetic. 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.  14
    Michael Sheard (1983). Indecomposable Ultrafilters Over Small Large Cardinals. Journal of Symbolic Logic 48 (4):1000-1007.
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  6.  1
    Michael Sheard (1995). Gupta Anil and Belnap Nuel. The Revision Theory of Truth. Bradford Books. The MIT Press, Cambridge, Mass., and London, 1993, Xii + 299 Pp. [REVIEW] Journal of Symbolic Logic 60 (4):1314-1316.
  7.  12
    Michael Sheard (1985). Co-Critical Points of Elementary Embeddings. Journal of Symbolic Logic 50 (1):220-226.
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    Michael Sheard (1995). Review: Anil Gupta, Nuel Belnap, The Revision Theory of Truth. [REVIEW] Journal of Symbolic Logic 60 (4):1314-1316.
  9. Michael Sheard (2015). Truth and Trustworthiness. In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Netherlands
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