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William Mitchell
University of Alabama, Birmingham
  1. The Reconfigured Eye: Visual Truth in the Post-Photographic Era.William J. Mitchell - 1994 - MIT Press.
    Continuing William Mitchell's investigations of how we understand, reason about, anduse images, The Reconfigured Eye provides the first systematic, critical analysis of the digitalimaging revolution.
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  2.  41
    Sets Constructible From Sequences of Ultrafilters.William J. Mitchell - 1974 - Journal of Symbolic Logic 39 (1):57-66.
    In [4], Kunen used iterated ultrapowers to show that ifUis a normalκ-complete nontrivial ultrafilter on a cardinalκthenL[U], the class of sets constructive fromU, has only the ultrafilterU∩L[U] and this ultrafilter depends only onκ. In this paper we extend Kunen's methods to arbitrary sequencesUof ultrafilters and obtain generalizations of these results. In particular we answer Problem 1 of Kunen and Paris [5] which asks whether the number of ultrafilters onκcan be intermediate between 1 and 22κ. If there is a normalκ-complete ultrafilterUonκsuch (...)
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  3.  22
    Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis.Moti Gitik & William J. Mitchell - 1996 - Annals of Pure and Applied Logic 82 (3):273-316.
    We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for (...)
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  4.  32
    On the Hamkins Approximation Property.William J. Mitchell - 2006 - Annals of Pure and Applied Logic 144 (1-3):126-129.
    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 ω2-Aronszajn 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.
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  5. Sets Constructed From Sequences of Measures: Revisited.William J. Mitchell - 1983 - Journal of Symbolic Logic 48 (3):600-609.
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  6.  43
    Adding Closed Unbounded Subsets of Ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
    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 ω₂-Aronszajn tree and to add an ω₂-Souslin tree with finite conditions.
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  7. A Weak Variation of Shelah's I[Ω₂].William J. Mitchell - 2004 - Journal of Symbolic Logic 69 (1):94-100.
    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.
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  8. The Late Derrida.William John Thomas Mitchell & Arnold Ira Davidson (eds.) - 2007 - University of Chicago Press.
    The rubric “The Late Derrida,” with all puns and ambiguities cheerfully intended, points to the late work of Jacques Derrida, the vast outpouring of new writing by and about him in the period roughly from 1994 to 2004. In this period Derrida published more than he had produced during his entire career up to that point. At the same time, this volume deconstructs the whole question of lateness and the usefulness of periodization. It calls into question the “fact” of his (...)
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  9.  40
    Bank Ethics: An Exploratory Study of Ethical Behaviors and Perceptions in Small, Local Banks. [REVIEW]William J. Mitchell, Phillip V. Lewis & N. L. Reinsch - 1992 - Journal of Business Ethics 11 (3):197 - 205.
    This article addresses five research questions: What specific behaviors are described in the literature as ethical or unethical? What percentage of business people are believed to be guilty of unethical behavior? What specific unethical behaviors have been observed by bank employees? How serious are the behaviors? Are experiences and attitudes affected by demographics? Conclusions suggest: There are seventeen categories of behavior, and that they are heavily skewed toward internal behaviors. Younger employees have a higher level of ethical consciousness than older (...)
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  10.  16
    Some Examples of Precipitous Ideals.Thomas J. Jech & William J. Mitchell - 1983 - Annals of Pure and Applied Logic 24 (2):131-151.
  11. The Complexity of the Core Model.William J. Mitchell - 1998 - Journal of Symbolic Logic 63 (4):1393-1398.
    If there is no inner model with a cardinal κ such that o(κ) = κ ++ then the set K ∩ H ω 1 is definable over H ω 1 by a Δ 4 formula, and the set $\{J_\alpha[\mathscr{U}]: \alpha of countable initial segments of the core model K = L[U] is definable over H ω 1 by a Π 3 formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model (...)
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  12. A Gitik Iteration with Nearly Easton Factoring.William J. Mitchell - 2003 - Journal of Symbolic Logic 68 (2):481-502.
    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 (...)
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  13. Extender Based Forcings.Moti Gitik, Menachem Magidor & William J. Mitchell - 2003 - Bulletin of Symbolic Logic 9 (2):237-241.
     
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  14. I[Ω₂] Can Be the Nonstationary Ideal on Cof. Transactions of the American Mathematical Society, Vol. 361.William J. Mitchell - 2011 - Bulletin of Symbolic Logic 17 (4):535-537.
  15. Covering Properties of Core Models.Ernest Schimmerling, Peter Koepke, William J. Mitchell & John R. Steel - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  16. Pictorial Turn. Eine Antwort.William Jt Mitchell - 2007 - In Hans Belting (ed.), Bilderfragen: Die Bildwissenschaften Im Aufbruch. Fink.
     
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  17.  12
    Pictorial turn. Una risposta.William J. T. Mitchell - 2012 - Lebenswelt: Aesthetics and Philosophy of Experience 2:130-143.
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  18.  15
    The Sharp for the Chang Model is Small.William J. Mitchell - 2017 - Archive for Mathematical Logic 56 (7-8):935-982.
    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 \.
    No categories
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  19.  14
    An Infinitary Ramsey Property.William J. Mitchell - 1992 - Annals of Pure and Applied Logic 57 (2):151-160.
    Mitchell, W.J., An infinitary Ramsey property, Annals of Pure and Applied Logic 57 151–160. We prove that the consistency of a measurable cardinal implies the consistency of a cardinal κ>+ satisfying the partition relations κ ω and κ ωregressive. This result follows work of Spector which uses the same hypothesis to prove the consistency of ω1 ω. We also give some examples of partition relations which can be proved for ω1 using the methods of Spector but cannot be proved for (...)
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  20.  12
    Gainesville, Florida March 10–13, 2007.Michael Benedikt, Andreas Blass, Natasha Dobrinen, Noam Greenberg, Denis R. Hirschfeldt, Salma Kuhlmann, Hannes Leitgeb, William J. Mitchell & Thomas Wilke - 2007 - Bulletin of Symbolic Logic 13 (3).
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  21. Urban Life, Jim—But Not As We Know It.William J. Mitchell - 2000 - Utopian Studies 11 (2):280-282.