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Joseph S. Miller [35]Joseph Len Miller [4]Joseph Hillis Miller [3]Joseph Dana Miller [3]
Joseph Miller [3]Joseph G. Miller [2]Joseph D. Miller [1]Joseph Michael Miller [1]

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Joseph Miller
Illinois Institute of Technology
Joseph Len Miller
West Chester University
  1.  21
    Universal computably enumerable equivalence relations.Uri Andrews, Steffen Lempp, Joseph S. Miller, Keng Meng Ng, Luca San Mauro & Andrea Sorbi - 2014 - Journal of Symbolic Logic 79 (1):60-88.
  2.  50
    Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
    It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be hard, (...)
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  3.  21
    The Undecidability of Iterated Modal Relativization.Joseph S. Miller & Lawrence S. Moss - 2005 - Studia Logica 79 (3):373-407.
    In dynamic epistemic logic and other fields, it is natural to consider relativization as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the transitive closure operation, due to its connection to common knowledge. We show that for three fragments of the logic of iterated relativization and transitive closure, the satisfiability problems are fi1 11–complete. Two of these fragments (...)
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  4.  18
    Relativizing chaitin's halting probability.Rod Downey, Denis R. Hirschfeldt, Joseph S. Miller & André Nies - 2005 - Journal of Mathematical Logic 5 (02):167-192.
    As a natural example of a 1-random real, Chaitin proposed the halting probability Ω of a universal prefix-free machine. We can relativize this example by considering a universal prefix-free oracle machine U. Let [Formula: see text] be the halting probability of UA; this gives a natural uniform way of producing an A-random real for every A ∈ 2ω. It is this operator which is our primary object of study. We can draw an analogy between the jump operator from computability theory (...)
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  5.  75
    For Derrida.Joseph Hillis Miller - 2009 - Fordham University Press.
    1. A Profession of Faith -- 2. Who or What Decides, for Derrida : A Catastrophic Theory of Decision -- 3. Derrida's Destinerrance -- 4. The Late Derrida -- 5. Derrida's Remains -- 6. Derrida Enisled -- 7. Derrida's Special Theory of Performativity --8. "Don't Count Me In" : Derrida's Refraining -- 9. Derrida's Ethics of Irresponsibilization ; or, How to Get Irresponsible, in Two Easy Lessons -- 10. Derrida's Politics of Autoimmunity -- 11. Touching Derrida's Touching Nancy -- 12. (...)
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  6.  11
    Density of the cototal enumeration degrees.Joseph S. Miller & Mariya I. Soskova - 2018 - Annals of Pure and Applied Logic 169 (5):450-462.
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  7.  30
    The K -Degrees, Low for K Degrees,and Weakly Low for K Sets.Joseph S. Miller - 2009 - Notre Dame Journal of Formal Logic 50 (4):381-391.
    We call A weakly low for K if there is a c such that $K^A(\sigma)\geq K(\sigma)-c$ for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K if and only if Chaitin's Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely (...)
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  8.  44
    Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.
    We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.
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  9.  5
    A structural dichotomy in the enumeration degrees.Hristo A. Ganchev, Iskander Sh Kalimullin, Joseph S. Miller & Mariya I. Soskova - 2022 - Journal of Symbolic Logic 87 (2):527-544.
    We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half of a nontrivial relativized $\mathcal {K}$ -pair. This leads to a structural dichotomy in the enumeration degrees.
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  10.  23
    Kolmogorov–Loveland randomness and stochasticity.Wolfgang Merkle, Joseph S. Miller, André Nies, Jan Reimann & Frank Stephan - 2006 - Annals of Pure and Applied Logic 138 (1):183-210.
    An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...)
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  11.  20
    Speech Acts in Literature.Joseph Hillis Miller - 2001 - Stanford University Press.
    This book demonstrates the presence of literature within speech act theory and the utility of speech act theory in reading literary works. Though the founding text of speech act theory, J. L. Austin's _How to Do Things with Words_, repeatedly expels literature from the domain of felicitous speech acts, literature is an indispensable presence within Austin's book. It contains many literary references but also uses as essential tools literary devices of its own: imaginary stories that serve as examples and imaginary (...)
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  12.  32
    Lowness for Kurtz randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.
    We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. (...)
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  13.  21
    Computing k-trivial sets by incomplete random sets.Laurent Bienvenu, Adam R. Day, Noam Greenberg, Antonín Kučera, Joseph S. Miller, André Nies & Dan Turetsky - 2014 - Bulletin of Symbolic Logic 20 (1):80-90.
    EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.
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  14. Every 2-random real is Kolmogorov random.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (3):907-913.
    We study reals with infinitely many incompressible prefixes. Call $A \in 2^{\omega}$ Kolmogorot random if $(\exists^{\infty}n) C(A \upharpoonright n) \textgreater n - \mathcal{O}(1)$ , where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by $Martin-L\ddot{0}f$ , Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse-proved by Nies. Stephan and Terwijn [11]-this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.
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  15. Etemeyaske Vpokat (Living Together Peacefully): How the Muscogee Concept of Harmony Can Provide a Structure to Morality.Joseph Len Miller - 2019 - In Colin Marshall (ed.), Comparative Metaethics: Neglected Perspectives on the Foundations of Morality. New York, USA: Routledge. pp. 81-101.
    Drawing primarily from the cultural traditions and beliefs of the Muscogee peoples, I will provide an account of how harmony can play a foundational role in providing a structure to morality. In the process of providing this account, I will begin (§2) by defining two key Muscogee concepts: ‘energy’ (§2.1) and ‘harmony’ (§2.2). I will also explain how the relationship between these two concepts can provide a structure for morality. Then I will explain the conditions that make promoting harmony a (...)
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  16.  10
    Denjoy, Demuth and density.Laurent Bienvenu, Rupert Hölzl, Joseph S. Miller & André Nies - 2014 - Journal of Mathematical Logic 14 (1):1450004.
    We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy–Young–Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class.
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  17.  24
    Degrees of Unsolvability of Continuous Functions.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (2):555 - 584.
    We show that the Turing degrees are not sufficient to measure the complexity of continuous functions on [0, 1]. Computability of continuous real functions is a standard notion from computable analysis. However, no satisfactory theory of degrees of continuous functions exists. We introduce the continuous degrees and prove that they are a proper extension of the Turing degrees and a proper substructure of the enumeration degrees. Call continuous degrees which are not Turing degrees non-total. Several fundamental results are proved: a (...)
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  18.  5
    A structural dichotomy in the enumeration degrees.Hristo A. Ganchev, Iskander Sh Kalimullin, Joseph S. Miller & Mariya I. Soskova - 2020 - Journal of Symbolic Logic:1-18.
    We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half a nontrivial relativized K-pair. This leads to a structural dichotomy in the enumeration degrees.
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  19.  4
    Randomness and lowness notions via open covers.Laurent Bienvenu & Joseph S. Miller - 2012 - Annals of Pure and Applied Logic 163 (5):506-518.
  20.  10
    Connected choice and the Brouwer fixed point theorem.Vasco Brattka, Stéphane Le Roux, Joseph S. Miller & Arno Pauly - 2019 - Journal of Mathematical Logic 19 (1):1950004.
    We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...)
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  21.  5
    Expanding the Reals by Continuous Functions Adds No Computational Power.Uri Andrews, Julia F. Knight, Rutger Kuyper, Joseph S. Miller & Mariya I. Soskova - forthcoming - Journal of Symbolic Logic:1-19.
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  22. Decolonizing the demarcation of the ethical.Joseph Len Miller - 2020 - Philosophical Studies 177 (2):337-352.
    The question of what distinguishes moral problems from other problems is important to the study of the evolution and functioning of morality. Many researchers concerned with this topic have assumed, either implicitly or explicitly, that all moral problems are problems of cooperation. This assumption offers a response to the moral demarcation problem by identifying a necessary condition of moral problems. Characterizing moral problems as problems of cooperation is a popular response to this issue – especially among researchers empirically studying the (...)
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  23.  5
    Maximal Towers and Ultrafilter Bases in Computability Theory.Steffen Lempp, Joseph S. Miller, André Nies & Mariya I. Soskova - forthcoming - Journal of Symbolic Logic:1-21.
    The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory. We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each (...)
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  24.  6
    Pa Relative to an Enumeration Oracle.Jun le Goh, Iskander Sh Kalimullin, Joseph S. Miller & Mariya I. Soskova - forthcoming - Journal of Symbolic Logic:1-29.
    Recall that B is PA relative to A if B computes a member of every nonempty $\Pi ^0_1(A)$ class. This two-place relation is invariant under Turing equivalence and so can be thought of as a binary relation on Turing degrees. Miller and Soskova [23] introduced the notion of a $\Pi ^0_1$ class relative to an enumeration oracle A, which they called a $\Pi ^0_1{\left \langle {A}\right \rangle }$ class. We study the induced extension of the relation B is PA relative (...)
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  25. Metaethical Agnosticism: Practical Reasons for Acting When Agnostic About the Existence of Moral Reasons.Joseph Len Miller - 2020 - Journal of Value Inquiry 54 (1):59-75.
    There has been little discussion about how to act when uncertain about the existence of moral reasons in general. In this paper I will argue that despite being uncertain about the existence of moral reasons, someone can still have a practical reason to act in a particular way. This practical reason is morally relevant because it will have an impact on whether we’re making the correct moral decision. This practical reason will result from a principle of decision-making that can be (...)
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  26.  51
    Book Review: Indigenizing Philosophy Through the Land: A Trickster Methodology for Decolonizing Environmental Ethics and Indigenous Futures by Brian Burkhart. [REVIEW]Joseph Len Miller - 2020 - APA Newsletter on Native American and Indigenous Philosophy 19 (2):7-11.
  27.  21
    Lowness for effective Hausdorff dimension.Steffen Lempp, Joseph S. Miller, Keng Meng Ng, Daniel D. Turetsky & Rebecca Weber - 2014 - Journal of Mathematical Logic 14 (2):1450011.
    We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension (...)
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  28. Effectiveness for infinite variable words and the Dual Ramsey Theorem.Joseph S. Miller & Reed Solomon - 2004 - Archive for Mathematical Logic 43 (4):543-555.
    We examine the Dual Ramsey Theorem and two related combinatorial principles VW(k,l) and OVW(k,l) from the perspectives of reverse mathematics and effective mathematics. We give a statement of the Dual Ramsey Theorem for open colorings in second order arithmetic and formalize work of Carlson and Simpson [1] to show that this statement implies ACA 0 over RCA 0 . We show that neither VW(2,2) nor OVW(2,2) is provable in WKL 0 . These results give partial answers to questions posed by (...)
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  29.  15
    On self-embeddings of computable linear orderings.Rodney G. Downey, Carl Jockusch & Joseph S. Miller - 2006 - Annals of Pure and Applied Logic 138 (1):52-76.
    The Dushnik–Miller Theorem states that every infinite countable linear ordering has a nontrivial self-embedding. We examine computability-theoretical aspects of this classical theorem.
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  30.  23
    Randomness and Halting Probabilities.VeróNica Becher, Santiago Figueira, Serge Grigorieff & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (4):1411 - 1430.
    We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ sets (...)
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  31.  59
    Two More Characterizations of K-Triviality.Noam Greenberg, Joseph S. Miller, Benoit Monin & Daniel Turetsky - 2018 - Notre Dame Journal of Formal Logic 59 (2):189-195.
    We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...)
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  32.  11
    The degrees of bi-hyperhyperimmune sets.Uri Andrews, Peter Gerdes & Joseph S. Miller - 2014 - Annals of Pure and Applied Logic 165 (3):803-811.
    We study the degrees of bi-hyperhyperimmune sets. Our main result characterizes these degrees as those that compute a function that is not dominated by any ∆02 function, and equivalently, those that compute a weak 2-generic. These characterizations imply that the collection of bi-hhi Turing degrees is closed upwards.
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  33.  53
    Daniel Graham. Science before Socrates: Parmenides, Anaxagoras, and the New Astronomy. Oxford: Oxford University Press, 2013. Pp. 304. $49.95. [REVIEW]Joseph G. Miller - 2014 - Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (1):212-215.
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  34. Difficulties of Democracy.Joseph Dana Miller - 1914 - International Journal of Ethics 25:213.
  35. Is Literary Theory a Science?Joseph Hillis Miller - 1993 - In George Levine (ed.), Realism and Representation. University of Wisconsin Press.
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  36.  7
    Computability and the Symmetric Difference Operator.Uri Andrews, Peter M. Gerdes, Steffen Lempp, Joseph S. Miller & Noah D. Schweber - 2022 - Logic Journal of the IGPL 30 (3):499-518.
    Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.
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  37.  29
    Phillip Sidney Horky. Plato and Pythagoreanism. Oxford: Oxford University Press, 2013. Pp. 320. £47.99. [REVIEW]Joseph G. Miller - 2014 - Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (2):391-393.
  38.  33
    Every 1-Generic Computes a Properly 1-Generic.Barbara F. Csima, Rod Downey, Noam Greenberg, Denis R. Hirschfeldt & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (4):1385 - 1393.
    A real is called properly n-generic if it is n-generic but not n+1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.
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  39.  25
    Moscone Center West, San Francisco, CA January 15–16, 2010.Fernando J. Ferreira, John Harrison, François Loeser, Chris Miller, Joseph S. Miller, Slawomir J. Solecki, Stevo Todorcevic & John Steel - 2010 - Bulletin of Symbolic Logic 16 (3).
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  40.  23
    Madison, WI, USA March 31–April 3, 2012.Alan Dow, Isaac Goldbring, Warren Goldfarb, Joseph Miller, Toniann Pitassi, Antonio Montalbán, Grigor Sargsyan, Sergei Starchenko & Moshe Vardi - 2013 - Bulletin of Symbolic Logic 19 (2).
  41.  30
    Peng Shuzhi and the Chinese Revolution: Notes Toward a Political Biography.Joseph T. Miller - 2001 - Historical Materialism 8 (1):265-266.
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  42.  12
    Nullifying randomness and genericity using symmetric difference.Rutger Kuyper & Joseph S. Miller - 2017 - Annals of Pure and Applied Logic 168 (9):1692-1699.
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  43.  6
    Computing from projections of random points.Noam Greenberg, Joseph S. Miller & André Nies - 2019 - Journal of Mathematical Logic 20 (1):1950014.
    We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...)
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  44.  13
    CS-UCS presentations and a lever: Human autoshaping.W. Gregg Wilcove & Joseph C. Miller - 1974 - Journal of Experimental Psychology 103 (5):868.
  45.  5
    Chaitin’s ω as a continuous function.Rupert Hölzl, Wolfgang Merkle, Joseph Miller, Frank Stephan & Liang Yu - 2020 - Journal of Symbolic Logic 85 (1):486-510.
    We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal (...)
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  46.  8
    Córdoba, Argentina September 20–24, 2004.Joos Heintz, Antonın Kucera, Joseph Miller, André Nies, Jan Reimann, Theodore Slaman, Diego Vaggione, Paul Vitányi & Verónica Becher - 2005 - Bulletin of Symbolic Logic 11 (4).
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  47.  7
    Unit activity of anterior cingulate cortex in differential conditioning and reversal.Michael Gabriel, Steven E. Saltwick & Joseph D. Miller - 1977 - Bulletin of the Psychonomic Society 9 (3):207-210.
  48.  5
    The upward closure of a perfect thin class.Rod Downey, Noam Greenberg & Joseph S. Miller - 2008 - Annals of Pure and Applied Logic 156 (1):51-58.
    There is a perfect thin class whose upward closure in the Turing degrees has full measure . Thus, in the Muchnik lattice of classes, the degree of 2-random reals is comparable with the degree of some perfect thin class. This solves a question of Simpson [S. Simpson, Mass problems and randomness, Bulletin of Symbolic Logic 11 1–27].
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  49.  13
    The difficulties of democracy.Joseph Dana Miller - 1915 - International Journal of Ethics 25 (2):213-225.
  50.  9
    The Difficulties of Democracy.Joseph Dana Miller - 1915 - International Journal of Ethics 25 (2):213-225.