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  1. Philip D. Welch (forthcoming). Bounded Martin's Maximum, Weak Erdos Cardinals, and AC. Journal of Symbolic Logic.
     
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  2. Peter Koepke & Philip D. Welch (2011). Global Square and Mutual Stationarity at the ℵn. Annals of Pure and Applied Logic 162 (10):787-806.
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  3. 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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  4. 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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  5. Philip D. Welch & Joel David Hamkins (2003). Pf ≠ NPf for Almost All F. Mathematical Logic Quarterly 49 (5):536.
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  6. 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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  7. 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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