
15The Ends of Theory: The Beijing Symposium on Critical InquiryCritical Inquiry 31 (2): 265. 2005.

23Medium Theory: Preface to the 2003 "Critical Inquiry" SymposiumCritical Inquiry 30 (2): 324. 2004.

20D. A. Martin and J. R. Steel. Iteration trees. Journal of the American Mathematical Society, vol. 7 , pp. 1–73 (review)Bulletin of Symbolic Logic 8 (4): 545546. 2002.

13Does God roll dice? Neutrality and determinism in evolutionary ecologyBiology and Philosophy 34 (1): 3. 2019.A tension between perspectives that emphasize deterministic versus stochastic processes has sparked controversy in ecology since preDarwinian times. The most recent manifestation of the contrasting perspectives arose with Hubbell’s proposed “neutral theory”, which hypothesizes a paramount role for stochasticity in ecological community composition. Here we shall refer to the deterministic and the stochastic perspectives as the nichebased and neutralbased research programs, respectively. Our go…Read more

4The sharp for the Chang model is smallArchive for Mathematical Logic 56 (78): 935982. 2017.Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the Chang model using only the existence of a cardinal \ having an extender of length \.

I[ω₂] can be the nonstationary ideal on Cof. Transactions of the American Mathematical Society, vol. 361Bulletin of Symbolic Logic 17 (4): 535537. 2011.

19Animal Rites: American Culture, the Discourse of Species, and Posthumanist TheoryUniversity of Chicago Press. 2003.In Animal Rites, Cary Wolfe examines contemporary notions of humanism and ethics by reconstructing a little known but crucial underground tradition of theorizing the animal from Wittgenstein, Cavell, and Lyotard to Lévinas, Derrida, ...

9On the Hamkins approximation propertyAnnals of Pure and Applied Logic 144 (1): 126129. 2006.We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property

14Review: D. A. Martin, J. R. Steel, Iteration Trees (review)Bulletin of Symbolic Logic 8 (4): 545546. 2002.

37Adding Closed Unbounded Subsets of ω₂ with Finite ForcingNotre Dame Journal of Formal Logic 46 (3): 357371. 2005.An outline is given of the proof that the consistency of a κ⁺Mahlo cardinal implies that of the statement that I[ω₂] does not include any stationary subsets of Cof(ω₁). An additional discussion of the techniques of this proof includes their use to obtain a model with no ω₂Aronszajn tree and to add an ω₂Souslin tree with finite conditions

173A weak variation of Shelah's I[ω₂]Journal of Symbolic Logic 69 (1): 94100. 2004.We use a $\kappa^{+}Mahlo$ cardinal to give a forcing construction of a model in which there is no sequence $\langle A_{\beta} : \beta \textless \omega_{2} \rangle$ of sets of cardinality $\omega_{1}$ such that $\{\lambda \textless \omega_{2} : \existsc \subset \lambda & (\bigcupc = \lambda otp(c) = \omega_{1} & \forall \beta \textless \lambda (c \cap \beta \in A_{\beta}))\}$ is stationary

164A Gitik iteration with nearly Easton factoringJournal of Symbolic Logic 68 (2): 481502. 2003.We reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can be factored in V as $R_{\kappa + 1} = R_{\lambda + 1} \times R_{\lambda + 1, \kappa}$ w…Read more

University of Alabama, BirminghamUndergraduate
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