31 found
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Philip Welch [24]Philip D. Welch [7]
  1.  74
    Salvatore Florio, Øystein Linnebo, Sean Walsh & Philip Welch (2015). Introduction. Notre Dame Journal of Formal Logic 56 (1):1-2.
    Introduction to a special issue based on a summer school on set theory and high-order logic.
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  2.  25
    Leon Horsten, Graham E. Leigh, Hannes Leitgeb & Philip Welch (2012). Revision Revisited. Review of Symbolic Logic 5 (4):642-664.
    This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
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  3.  78
    Volker Halbach, Hannes Leitgeb & Philip Welch (2003). Possible-Worlds Semantics for Modal Notions Conceived as Predicates. Journal of Philosophical Logic 32 (2):179-223.
    If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...)
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  4.  35
    Leon Horsten & Philip Welch (2007). The Undecidability of Propositional Adaptive Logic. Synthese 158 (1):41 - 60.
    We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and (...)
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  5.  30
    Benedikt Löwe & Philip D. Welch (2001). Set-Theoretic Absoluteness and the Revision Theory of Truth. 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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  6.  9
    Sy-David Friedman, Philip Welch & W. Woodin (2008). On the Consistency Strength of the Inner Model Hypothesis. Journal of Symbolic Logic 73 (2):391-400.
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  7.  16
    Philip D. Welch (2004). On the Possibility, or Otherwise, of Hypercomputation. 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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  8.  8
    Philip D. Welch (2011). Discrete Transfinite Computation Models. In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific 375--414.
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  9.  17
    Kai-Uwe Kühnberger, Benedikt Löwe, Michael Möllerfeld & Philip Welch (2005). Comparing Inductive and Circular Definitions: Parameters, Complexity and Games. Studia Logica 81 (1):79 - 98.
    Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.
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  10.  17
    Sy-David Friedman, Philip Welch & W. Hugh Woodin (2008). On the Consistency Strength of the Inner Model Hypothesis. Journal of Symbolic Logic 73 (2):391 - 400.
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  11.  17
    Philip D. Welch & Joel David Hamkins (2003). Pf ≠ NPf for Almost All F. Mathematical Logic Quarterly 49 (5):536.
    We discuss the question of Ralf-Dieter Schindler whether for infinite time Turing machines Pf = NPf can be true for any function f from the reals into ω1. We show that “almost everywhere” the answer is negative.
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  12.  13
    Philip Welch (1985). Comparing Incomparable Kleene Degrees. Journal of Symbolic Logic 50 (1):55-58.
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  13. Leon Horsten & Philip Welch (2007). The Undecidability of Propositional Adaptive Logic. Synthese 158 (1):41-60.
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  14.  8
    Philip Welch (1987). The Reals in Core Models. Journal of Symbolic Logic 52 (1):64-67.
    We set $\mathscr{D} = \langle\mathscr{D}, \leq_L, \tt\#\rangle$ , where D is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in K, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals.
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  15.  11
    David Asperó & Philip D. Welch (2002). Bounded Martin's Maximum, Weak [Image] Cardinals, and [Image]. 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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  16.  5
    Philip Welch (1987). Minimality in the ▵13-Degrees. Journal of Symbolic Logic 52 (4):908 - 915.
    We show in ZFC, assuming all reals have sharps, that a countable collection of ▵ 1 3 -degrees without a minimal upper bound implies the existence of inner models with measurable cardinals.
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  17. Philip Welch (2005). Kai–Uwe Kühnberger Benedikt Löwe Michael Möllerfeld. Studia Logica 81:79-98.
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  18.  1
    Leon Horsten & Philip Welch (2009). The Undecidability of Propositional Adaptive Logic. Synthese 169 (1):217-218.
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  19.  6
    Leon Horsten & Philip Welch (2009). Erratum: The Undecidability of Propositional Adaptive Logic. Synthese 169 (1):217 - 218.
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  20.  1
    Peter Koepke & Philip D. Welch (2011). Global Square and Mutual Stationarity at the ℵn. 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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  21.  7
    Philip Welch (1986). The Natural Hierarchy and Quasi-Hierarchy of Constructibility Degrees. Journal of Symbolic Logic 51 (1):130-134.
    We investigate the set S 2 of "quickly sharped" reals: \begin{align*}S_2 &= \{x \mid x \in M, M \text{the} <^\ast-\text{least mouse} \not\in L\lbrack x\rbrack\} \\ &= \{x \mid L\lbrack x\rbrack \models "V = K"\},\\ \end{align*} in the manner of [K] defining a natural hierarchy and quasi-hierarchy of constructibility degrees and identifying their termination points.
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  22.  1
    Philip Welch (1995). Review: Menachem Magidor, Representing Sets of Ordinals as Countable Unions of Sets in the Core Model. [REVIEW] Journal of Symbolic Logic 60 (2):701-704.
  23.  1
    Philip Welch (1990). Review: Sy D. Friedman, Strong Coding; Sy D. Friedman, A Guide to "Strong Coding.". [REVIEW] Journal of Symbolic Logic 55 (3):1311-1313.
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  24. Peter Holy, Philip Welch & Liuzhen Wu (2015). Local Club Condensation and L-Likeness. Journal of Symbolic Logic 80 (4):1361-1378.
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  25. Leon Horsten & Philip Welch (eds.) (2016). Godel's Disjunction: The Scope and Limits of Mathematical Knowledge. Oxford University Press Uk.
    To what extent can we hope to find answers to all mathematical questions? A famous theorem from Gödel entails that if our thinking capacities do not go beyond what an electronic computer is capable of, then there are indeed absolutely unsolvable mathematical problems. Thus it is of capital importance to find out whether human mathematicians can outstrip computers. Within this context, the contributions to this book critically examine positions about the scope and limits of human mathematical knowledge.
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  26. David Asperó & Philip D. Welch (2002). Bounded Martin's Maximum, Weak Erdӧs Cardinals, and Ψ Ac. Journal of Symbolic Logic 67 (3):1141-1152.
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  27. Philip Welch (1990). Friedman Sy D.. Strong Coding. Annals of Pure and Applied Logic, Vol. 35 (1987), Pp. 1–98. Friedman Sy D.. A Guide to “Strong Coding.” Annals of Pure and Applied Logic, Vol. 35 (1987), Pp. 99–122. [REVIEW] Journal of Symbolic Logic 55 (3):1311-1313.
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  28. Philip Welch (1987). Minimality in the $Triangle^1_3$-Degrees. Journal of Symbolic Logic 52 (4):908-915.
    We show in ZFC, assuming all reals have sharps, that a countable collection of $\triangle^1_3$-degrees without a minimal upper bound implies the existence of inner models with measurable cardinals.
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  29. Philip Welch (1987). Minimality in the Δ⅓-Degrees. Journal of Symbolic Logic 52 (4):908-915.
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  30. Philip Welch (1995). Magidor Menachem. Representing Sets of Ordinals as Countable Unions of Sets in the Core Model. Transactions of the American Mathematical Society, Vol. 317 , Pp. 91–126. [REVIEW] Journal of Symbolic Logic 60 (2):701-704.
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  31. Philip Welch (2003). Set-Theoretic Absoluteness and the Revision Theory. Bulletin of Symbolic Logic 9 (2):235-237.