10 found
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  1.  17
    Some Observations on Truth Hierarchies: A Correction.Philip D. Welch - 2020 - Review of Symbolic Logic 13 (4):857-860.
    A correction is needed to our paper: to the definition contained within the statement of Lemma 1.5 and thus arguments around it in §3.
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  2.  56
    Set-Theoretic Absoluteness and the Revision Theory of Truth.Benedikt Löwe & Philip D. Welch - 2001 - Studia Logica 68 (1):21-41.
    We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.
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  3.  27
    On the Possibility, or Otherwise, of Hypercomputation.Philip D. Welch - 2004 - British Journal for the Philosophy of Science 55 (4):739-746.
    We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems to lead (...)
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  4.  13
    Discrete Transfinite Computation Models.Philip D. Welch - 2011 - In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific. pp. 375--414.
  5.  5
    Bounded Martin's Maximum, Weak Erdӧs Cardinals, and Ψ Ac.David Asperó & Philip D. Welch - 2002 - Journal of Symbolic Logic 67 (3):1141-1152.
  6.  5
    Closed and Unbounded Classes and the Härtig Quantifier Model.Philip D. Welch - 2022 - Journal of Symbolic Logic 87 (2):564-584.
    We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...)
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  7.  8
    The Ramified Analytical Hierarchy Using Extended Logics.Philip D. Welch - 2018 - Bulletin of Symbolic Logic 24 (3):306-318.
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  8.  19
    Bounded Martin's Maximum, Weak [Image] Cardinals, and [Image].David Asperó & Philip D. Welch - 2002 - Journal of Symbolic Logic 67 (3):1141 - 1152.
    We prove that a form of the $Erd\H{o}s$ property (consistent with $V = L\lbrack H_{\omega_2}\rbrack$ and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle $\psi_{AC}$ holds, and therefore 2ℵ0 = ℵ2. We also prove that $\psi_{AC}$ implies that every function $f: \omega_1 \rightarrow \omega_1$ is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum (...)
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  9.  9
    Global Square and Mutual Stationarity at the ℵn.Peter Koepke & Philip D. Welch - 2011 - Annals of Pure and Applied Logic 162 (10):787-806.
    We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which for (...)
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  10.  4
    Stably Measurable Cardinals.Philip D. Welch - 2021 - Journal of Symbolic Logic 86 (2):448-470.
    We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma _{1}$ -definability at uncountable regular cardinals. In particular we give its exact consistency strength first in terms of the second uniform indiscernible for bounded subsets of $\kappa $ : $u_2$, and secondly to give the consistency strength of a property of Lücke’s.TheoremThe following are equiconsistent:There exists $\kappa $ which is stably measurable;for some cardinal $\kappa $, $u_2=\sigma $ ;The $\boldsymbol {\Sigma }_{1}$ -club property holds (...)
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