Results for ' hyperarithmetic comprehension'

996 found
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  1.  45
    Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle.Chris Conidis, Noam Greenberg & Daniel Turetsky - 2013 - Notre Dame Journal of Formal Logic 54 (2):233-252.
    We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.
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  2. Ştefan afloroaei.Aurel Codoban, Despre Comprehensiune, REFLECŢIE CRITICĂ & On Comprehension - 2008 - Journal for the Study of Religions and Ideologies 7 (21):112-119.
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  3. Contrastes 11.Domaine Français Et la PassiviteItalien & I. Comprehension Et Interpretation - 1985 - Contrastes: Revue de l'Association Pour le Developpement des Études Contrastives 10:11.
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  4. Comparing Peano arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
    This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of (...)
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  5.  17
    On the Π1 1 -separation principle.Antonio Montalbán - 2008 - Mathematical Logic Quarterly 54 (6):563-578.
    We study the proof-theoretic strength of the Π11-separation axiom scheme, and we show that Π11-separation lies strictly in between the Δ11-comprehension and Σ11-choice axiom schemes over RCA0.
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  6.  14
    The strength of Jullien's indecomposability theorem.Itay Neeman - 2008 - Journal of Mathematical Logic 8 (1):93-119.
    Jullien's indecomposability theorem states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis. We identify the strength of the theorem relative to standard reverse mathematics markers. We show that it lies strictly between weak [Formula: see text] choice and [Formula: see text] comprehension.
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  7.  18
    Necessary use of [image] induction in a reversal.Itay Neeman - 2011 - Journal of Symbolic Logic 76 (2):561 - 574.
    Jullien's indecomposability theorem (INDEC) states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis, and then, in the base system RCA₀ plus ${\mathrm{\Sigma }}_{1}^{1}\text{\hspace{0.17em}}$ induction, it was shown by Neeman to have strength strictly between weak ${\mathrm{\Sigma }}_{1}^{1}$ choice and ${\mathrm{\Delta }}_{1}^{1}$ comprehension. We prove in this paper that ${\mathrm{\Sigma }}_{1}^{1}$ induction is (...)
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  8.  14
    The Strength of an Axiom of Finite Choice for Branches in Trees.G. O. H. Jun Le - 2023 - Journal of Symbolic Logic 88 (4):1367-1386.
    In their logical analysis of theorems about disjoint rays in graphs, Barnes, Shore, and the author (hereafter BGS) introduced a weak choice scheme in second-order arithmetic, called the $\Sigma ^1_1$ axiom of finite choice (hereafter finite choice). This is a special case of the $\Sigma ^1_1$ axiom of choice ( $\Sigma ^1_1\text {-}\mathsf {AC}_0$ ) introduced by Kreisel. BGS showed that $\Sigma ^1_1\text {-}\mathsf {AC}_0$ suffices for proving many of the aforementioned theorems in graph theory. While it is not known (...)
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  9.  13
    Intrinsically Hyperarithmetical Sets.Ivan N. Soskov - 1996 - Mathematical Logic Quarterly 42 (1):469-480.
    The main result proved in the paper is that on every recursive structure the intrinsically hyperarithmetical sets coincide with the relatively intrinsically hyperarithmetical sets. As a side effect of the proof an effective version of the Kueker's theorem on definability by means of infinitary formulas is obtained.
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  10.  15
    Hyperarithmetical relations in expansions of recursive structures.Alan D. Vlach - 1994 - Annals of Pure and Applied Logic 66 (2):163-196.
    Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a recursive (...)
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  11.  58
    Mass problems and hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
    A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if for all Y ∈ Q there exists X ∈ P such that X is Turing reducible to Y. A weak degree is an equivalence class of mass problems under mutual weak reducibility. Let [Formula: see text] be the lattice of weak degrees of mass problems associated with nonempty [Formula: see text] subsets of the Cantor (...)
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  12.  36
    Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures.Walker M. White & Denis R. Hirschfeldt - 2002 - Notre Dame Journal of Formal Logic 43 (1):51-64.
    We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or.
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  13.  15
    Almost Theorems of Hyperarithmetic Analysis.Richard A. Shore - forthcoming - Journal of Symbolic Logic:1-33.
    Theorems of hyperarithmetic analysis (THAs) occupy an unusual neighborhood in the realms of reverse mathematics and recursion theoretic complexity. They lie above all the fixed (recursive) iterations of the Turing Jump but below ATR $_{0}$ (and so $\Pi _{1}^{1}$ -CA $_{0}$ or the hyperjump). There is a long history of proof theoretic principles which are THAs. Until Barnes, Goh, and Shore [ta] revealed an array of theorems in graph theory living in this neighborhood, there was only one mathematical denizen. (...)
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  14.  45
    Indecomposable linear orderings and hyperarithmetic analysis.Antonio Montalbán - 2006 - Journal of Mathematical Logic 6 (1):89-120.
    A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y⊆ω, the minimum ω-model containing Y of RCA0 + S is HYP, the ω-model consisting of the sets hyperarithmetic in Y. We provide an example of a mathematical theorem which is a statement of hyperarithmetic analysis. This statement, that we call INDEC, is due to Jullien [13]. To the author's knowledge, no other already published, purely mathematical statement has been found (...)
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  15.  27
    Computable structures and the hyperarithmetical hierarchy.C. J. Ash - 2000 - New York: Elsevier. Edited by J. Knight.
    This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...)
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  16.  34
    An introduction to hyperarithmetical functions.Julia Robinson - 1967 - Journal of Symbolic Logic 32 (3):325-342.
  17.  23
    Relative to any non-hyperarithmetic set.Noam Greenberg, Antonio Montalbán & Theodore A. Slaman - 2013 - Journal of Mathematical Logic 13 (1):1250007.
    We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.
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  18.  9
    Theorems of hyperarithmetic analysis and almost theorems of hyperarithmetic analysis.James S. Barnes, Jun le Goh & Richard A. Shore - 2022 - Bulletin of Symbolic Logic 28 (1):133-149.
    Theorems of hyperarithmetic analysis occupy an unusual neighborhood in the realms of reverse mathematics and recursion-theoretic complexity. They lie above all the fixed iterations of the Turing jump but below ATR $_{0}$. There is a long history of proof-theoretic principles which are THAs. Until the papers reported on in this communication, there was only one mathematical example. Barnes, Goh, and Shore [1] analyze an array of ubiquity theorems in graph theory descended from Halin’s [9] work on rays in graphs. (...)
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  19.  50
    Up to Equimorphism, Hyperarithmetic Is Recursive.Antonio Montalbán - 2005 - Journal of Symbolic Logic 70 (2):360 - 378.
    Two linear orderings are equimorphic if each can be embedded into the other. We prove that every hyperarithmetic linear ordering is equimorphic to a recursive one. On the way to our main result we prove that a linear ordering has Hausdorff rank less than $\omega _{1}^{\mathit{CK}}$ if and only if it is equimorphic to a recursive one. As a corollary of our proof we prove that, given a recursive ordinal α, the partial ordering of equimorphism types of linear orderings (...)
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  20. Degrees of Categoricity and the Hyperarithmetic Hierarchy.Barbara F. Csima, Johanna N. Y. Franklin & Richard A. Shore - 2013 - Notre Dame Journal of Formal Logic 54 (2):215-231.
    We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures (...)
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  21.  10
    Elementary Formal Systems for Hyperarithmetical Relations.Melvin Fitting - 1978 - Mathematical Logic Quarterly 24 (1‐6):25-30.
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  22.  28
    Elementary Formal Systems for Hyperarithmetical Relations.Melvin Fitting - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (1-6):25-30.
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  23.  46
    A note on the hyperarithmetical hierarchy.H. B. Enderton & Hilary Putnam - 1970 - Journal of Symbolic Logic 35 (3):429-430.
  24. A Comprehensive Account of Blame: Self-Blame, Non-Moral Blame, and Blame for the Non-Voluntary.Douglas W. Portmore - 2022 - In Andreas Carlsson (ed.), Self-Blame and Moral Responsibility. New York, USA: Cambridge University Press.
    Blame is multifarious. It can be passionate or dispassionate. It can be expressed or kept private. We blame both the living and the dead. And we blame ourselves as well as others. What’s more, we blame ourselves, not only for our moral failings, but also for our non-moral failings: for our aesthetic bad taste, gustatory self-indulgence, or poor athletic performance. And we blame ourselves both for things over which we exerted agential control (e.g., our voluntary acts) and for things over (...)
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  25.  25
    Categoricity in hyperarithmetical degrees.C. J. Ash - 1987 - Annals of Pure and Applied Logic 34 (1):1-14.
  26. ASH, CJ, Categoricity in hyperarithmetical degrees BALDWIN, JT and HARRINGTON, L., Trivial pursuit: Re-marks on the main gap COOPER, SB and EPSTEIN, RL, Complementing below re-cursively enumerable degrees.J. Steprans & S. Shelah - 1987 - Annals of Pure and Applied Logic 34:311.
  27. The Comprehensibility of the Universe: A New Conception of Science.Nicholas Maxwell - 1998 - Oxford, GB: Oxford University Press UK.
    The Comprehensibility of the Universe puts forward a radically new conception of science. According to the orthodox conception, scientific theories are accepted and rejected impartially with respect to evidence, no permanent assumption being made about the world independently of the evidence. Nicholas Maxwell argues that this orthodox view is untenable. He urges that in its place a new orthodoxy is needed, which sees science as making a hierarchy of metaphysical assumptions about the comprehensibility and knowability of the universe, these assumptions (...)
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  28.  14
    A decidable Ehrenfeucht theory with exactly two hyperarithmetic models.Robert C. Reed - 1991 - Annals of Pure and Applied Logic 53 (2):135-168.
    Millar showed that for each n<ω, there is a complete decidable theory having precisely eighteen nonisomorphic countable models where some of these are decidable exactly in the hyperarithmetic set H. By combining ideas from Millar's proof with a technique of Peretyat'kin, the author reduces the number of countable models to five. By a theorem of Millar, this is the smallest number of countable models a decidable theory can have if some of the models are not 0″-decidable.
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  29. Comprehension, Demonstration, and Accuracy in Aristotle.Breno Zuppolini - 2020 - Journal of the History of Philosophy 58 (1):29-48.
    according to aristotle's posterior analytics, scientific expertise is composed of two different cognitive dispositions. Some propositions in the domain can be scientifically explained, which means that they are known by "demonstration", a deductive argument in which the premises are explanatory of the conclusion. Thus, the kind of cognition that apprehends those propositions is called "demonstrative knowledge".1 However, not all propositions in a scientific domain are demonstrable. Demonstrations are ultimately based on indemonstrable principles, whose knowledge is called "comprehension".2 If the (...)
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  30.  41
    Comprehension and computation in Bayesian problem solving.Eric D. Johnson & Elisabet Tubau - 2015 - Frontiers in Psychology 6:137658.
    Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...)
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  31.  4
    Martin’s conjecture for regressive functions on the hyperarithmetic degrees.Patrick Lutz - forthcoming - Journal of Mathematical Logic.
    We answer a question of Slaman and Steel by showing that a version of Martin’s conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin’s conjecture, consists of showing that we can always reduce to the case of a continuous function.
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  32. A Comprehensive Definition of Illocutionary Silencing.Laura Caponetto - 2021 - Topoi 40 (1):191-202.
    A recurring concern within contemporary philosophy of language has been with the ways in which speakers can be illocutionarily silenced, i.e. hindered in their capacity to do things with words. Moving beyond the traditional conception of silencing as uptake failure, Mary Kate McGowan has recently claimed that silencing may also involve other forms of recognition failure. In this paper I first offer a supportive elaboration of McGowan’s claims by developing a social account of speech act performance, according to which the (...)
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  33.  14
    Isomorphism types of the hyperarithmetic sets Ha.George C. Nelson - 1978 - Notre Dame Journal of Formal Logic 19:1.
  34.  30
    Comparing Comprehension of a Long Text Read in Print Book and on Kindle: Where in the Text and When in the Story?Anne Mangen, Gérard Olivier & Jean-Luc Velay - 2019 - Frontiers in Psychology 10.
    Digital reading devices such as Kindle differ from paper books with respect to the kinesthetic and tactile feedback provided to the reader, but the role of these features in reading is rarely studied empirically. This experiment compares reading of a long text on Kindle DX and in print. Fifty participants (24 years old) read a 28 page (approx. one hour reading time) long mystery story on Kindle or in a print pocket book and completed several tests measuring various levels of (...)
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  35. Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model.Jakub Szymanik & Marcin Zajenkowski - 2010 - Cognitive Science 34 (3):521-532.
    We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon hypothesis and (...)
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  36.  17
    Recursive linear orderings and hyperarithmetical functions.Shih-Chao Liu - 1962 - Notre Dame Journal of Formal Logic 3 (3):129-132.
  37.  12
    The comprehension and production of Wh- questions among Malay children with developmental language disorders: Climbing the syntactic tree.Norsofiah Abu Bakar, Giuditta Smith, Rogayah A. Razak & Maria Garraffa - 2022 - Frontiers in Psychology 13.
    This study is an investigation of both comprehension and production of Wh- questions in Malay-speaking children with a developmental language disorder. A total of 15 Malay children with DLD were tested on a set of Wh- questions, comparing their performance with two control groups [15 age-matched typically developing children and 15 younger TD language-matched children]. Malay children with DLD showed a clear asymmetry in comprehension of Wh- questions, with a selective impairment for which NP questions compared with who (...)
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  38.  59
    Comprehension and Recall of Informed Consent among Participating Families in a Birth Cohort Study on Diarrhoeal Disease.R. Sarkar, E. W. Grandin, B. P. Gladstone, J. Muliyil & G. Kang - 2009 - Public Health Ethics 2 (1):37-44.
    Comprehension and recall of informed consent was assessed after the study closure in the parents/guardians of a birth cohort of children participating in an intensive three-year diarrhoeal surveillance. A structured questionnaire was administered by field workers who had not participated in the study's follow-up protocol. Of 368 respondents, 329 (89.4 per cent) stated that the study was adequately explained during enrolment, but only 159 (43.2 per cent) could recall that it was on diarrhoea. Nearly half (45.9 per cent) of (...)
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  39.  42
    Comprehension of sentences by bottlenosed dolphins.Louis M. Herman, Douglas G. Richards & James P. Wolz - 1984 - Cognition 16 (2):129-219.
  40. Comprehensive or Political Liberalism? The Impartial Spectator and the Justification of Political Principles.Nir Ben-Moshe - 2021 - Utilitas 33 (3):253-269.
    John Rawls raises three challenges – to which one can add a fourth challenge – to an impartial spectator account: (a) the impartial spectator is a utility-maximizing device that does not take seriously the distinction between persons; (b) the account does not guarantee that the principles of justice will be derived from it; (c) the notion of impartiality in the account is the wrong one, since it does not define impartiality from the standpoint of the litigants themselves; (d) the account (...)
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  41.  38
    Comprehension and recall of informed consent among participating families in a birth cohort study on diarrhoeal disease.Rajiv Sarkar, Edward Wilson Grandin, Beryl Primrose Gladstone, Jayaprakash Muliyil & Gagandeep Kang - 2009 - Public Health Ethics 2 (1):37-44.
    Comprehension and recall of informed consent was assessed after the study closure in the parents/guardians of a birth cohort of children participating in an intensive three-year diarrhoeal surveillance. A structured questionnaire was administered by field workers who had not participated in the study's follow-up protocol. Of 368 respondents, 329 stated that the study was adequately explained during enrolment, but only 159 could recall that it was on diarrhoea. Nearly half of the respondents stated that they would not have participated (...)
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  42.  19
    Language comprehension in ape and child: evolutionary implications.E. S. Savage-Rumbaugh & E. Rubert - 1992 - In Y. Christen & P. S. Churchland (eds.), Neurophilosophy and Alzheimer's Disease. Springer Verlag. pp. 30--48.
  43.  10
    The Axiom of Choice and the Class of Hyperarithmetic Functions.G. Kreisel - 1970 - Journal of Symbolic Logic 35 (2):333-334.
  44.  13
    Enhancing comprehension of online informed consent: the impact of interactive elements and presentation formats.Bree Holtz, Katharine Mitchell, Robyn Adams, Caitlin Grier & Jason Wright - forthcoming - Ethics and Behavior.
    Informed consent, a cornerstone of research ethics, ensures participant protection and informed participation, particularly in online settings. Despite its significance, engagement with online consent forms remains low, underscoring the need for improved presentation strategies. This study investigates the impact of interactive elements and diverse presentation formats on the comprehension and engagement of online informed consent documents among a broad demographic beyond the commonly studied student populations. Employing a between-subjects experimental design, we explored six versions of online consent forms varying (...)
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  45. Back toward a Comprehensive Liberalism?Ruth Abbey - 2007 - Political Theory 35 (1):5-28.
    This article examines the attempts by John Rawls in the works published after Political Liberalism to engage with some of the feminist responses to his work. Rawls goes a long way toward addressing some of the major feministliberal concerns. Yet this has the unintended consequence of pushing justice as fairness in the direction of a more comprehensive, rather than a strictly political, form of liberalism. This does not seem to be a problem peculiar to Rawls: rather, any form of liberalism (...)
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  46.  17
    Comprehensive Reform of Japanese Personal Insolvency Law.Junichi Matsushita - 2006 - Theoretical Inquiries in Law 7 (2):555-564.
    The project of the comprehensive reform of Japanese insolvency law started in October 1996. After many enactments and amendments, there are now two types of judicial proceedings for personal insolvencies in Japanese insolvency law. The first category is straight bankruptcy proceedings in which the debtor can be discharged; the other is special Civil Rehabilitation proceedings for individual debtors. In this Article, I will first give a brief overview of the special Civil Rehabilitation proceedings for individual debtors, including a short description (...)
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  47.  30
    Comprehension and Informed Consent: Assessing the Effect of a Short Consent Form.Leanne Stunkel, Meredith Benson, Louise McLellan, Ninet Sinaii, Gabriella Bedarida, Ezekiel Emanuel & Christine Grady - 2010 - IRB: Ethics & Human Research 32 (4):1.
    The objective of this study—a substudy to a phase I bioequivalence study—was to compare the effect of standard and concise consent forms on research volunteers’ comprehension of and satisfaction with consent forms, as well as to assess the effect of select volunteer characteristics, such as financial motivations to participate in research, on their comprehension. A 36-item questionnaire measured volunteers’ comprehension, satisfaction, and motivations for participation. Volunteers were randomized to the standard Pfizer consent form or a concise, easier-to-read (...)
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  48.  95
    Naïve comprehension and contracting implications.Susan Rogerson & Sam Butchart - 2002 - Studia Logica 71 (1):119-132.
    In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall''s conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.
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  49. A comprehensive review of auditory verbal hallucinations: lifetime prevalence, correlates and mechanisms in healthy and clinical individuals.Saskia de Leede-Smith & Emma Barkus - 2013 - Frontiers in Human Neuroscience 7.
  50.  12
    Comprehensive Quality Assessment in Clinical Ethics.Joshua S. Crites, Flora Sheppard, Mark Repenshek, Janet Malek, Nico Nortjé, Matthew Kenney, Avery C. Glover, John Frye, Kristin Furfari, Evan G. DeRenzo, Cynthia Coleman, Andrea Chatburn & Thomas V. Cunningham - 2019 - Journal of Clinical Ethics 30 (3):284-296.
    Scholars and professional organizations in bioethics describe various approaches to “quality assessment” in clinical ethics. Although much of this work represents significant contributions to the literature, it is not clear that there is a robust and shared understanding of what constitutes “quality” in clinical ethics, what activities should be measured when tracking clinical ethics work, and what metrics should be used when measuring those activities. Further, even the most robust quality assessment efforts to date are idiosyncratic, in that they represent (...)
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