Results for 'p-adic numbers'

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  1.  10
    Expansions of the padic numbers that interpret the ring of integers.Nathanaël Mariaule - 2020 - Mathematical Logic Quarterly 66 (1):82-90.
    Let be the field of p‐adic numbers in the language of rings. In this paper we consider the theory of expanded by two predicates interpreted by multiplicative subgroups and where are multiplicatively independent. We show that the theory of this structure interprets Peano arithmetic if α and β have positive p‐adic valuation. If either α or β has zero valuation we show that the theory of has the NIP (“negation of the independence property”) and therefore does not (...)
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  2.  12
    One dimensional groups definable in the p-adic numbers.Juan Pablo Acosta López - 2021 - Journal of Symbolic Logic 86 (2):801-816.
    A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subgroup and a quotient by a finite subgroup.
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  3.  14
    The field of p-adic numbers with a predicate for the powers of an integer.Nathanaël Mariaule - 2017 - Journal of Symbolic Logic 82 (1):166-182.
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  4.  70
    Logics for Reasoning About Processes of Thinking with Information Coded by p-adic Numbers.Angelina Ilić Stepić & Zoran Ognjanović - 2015 - Studia Logica 103 (1):145-174.
    In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance (...)
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  5.  43
    A p-adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4):263-280.
    In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually (...)
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  6.  25
    More on definable sets of p-adic numbers.Philip Scowcroft - 1988 - Journal of Symbolic Logic 53 (3):912-920.
  7.  50
    A p‐adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4-5):263-280.
    In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually (...)
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  8.  69
    A version of p-adic minimality.Raf Cluckers & Eva Leenknegt - 2012 - Journal of Symbolic Logic 77 (2):621-630.
    We introduce a very weak language L M on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language L M are trivial functions. We also give a definitional expansion $L\begin{array}{*{20}{c}} ' \\ M \\ \end{array} $ of L M in which K has quantifier (...)
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  9.  15
    James Ax and Simon Kochen. Diophantine problems over local fields I. American journal of mathematics, vol. 87 , pp. 605–630. - James Ax and Simon Kochen. Diophantine problems over local fields II. A complete set of axioms for p-adic number theory. American journal of mathematics, vol. 87 , pp. 631–648. - James Ax and Simon Kochen. Diophantine problems over local fields III. Decidable fields. Annals of mathematics, vol. 83 , pp. 437–456. [REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):683-684.
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  10.  9
    Review: James Ax, Simon Kochen, Diophantine Problems Over Local Fields I; James Ax, Simon Kochen, Diophantine Problems Over Local Fields II. A Complete set of Axioms for $p$-adic number theory; James Ax, Simon Kochen, Diophantine Problems over Local Field III. Decidable Fields. [REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):683-684.
  11.  18
    p-Adic valued logical calculi in simulations of the slime mould behaviour.Andrew Schumann - 2015 - Journal of Applied Non-Classical Logics 25 (2):125-139.
    In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould, the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than attractants, then this behaviour can be coded in terms of p-adic numbers. As (...)
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  12.  91
    Cell decomposition for semibounded p-adic sets.Eva Leenknegt - 2013 - Archive for Mathematical Logic 52 (5-6):667-688.
    We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic (...)
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  13.  29
    A note on groups definable in the p -adic field.Anand Pillay & Ningyuan Yao - 2019 - Archive for Mathematical Logic 58 (7-8):1029-1034.
    It is known Hrushovski and Pillay that a group G definable in the field \ of p-adic numbers is definably locally isomorphic to the group \\) of p-adic points of a algebraic group H over \. We observe here that if H is commutative then G is commutative-by-finite. This shows in particular that any one-dimensional group G definable in \ is commutative-by-finite. This result extends to groups definable in p-adically closed fields. We prove our results in the (...)
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  14.  5
    Model completion of scaled lattices and co‐Heyting algebras of padic semi‐algebraic sets.Luck Darnière - 2019 - Mathematical Logic Quarterly 65 (3):305-331.
    Let p be prime number, K be a p‐adically closed field, a semi‐algebraic set defined over K and the lattice of semi‐algebraic subsets of X which are closed in X. We prove that the complete theory of eliminates quantifiers in a certain language, the ‐structure on being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field for. We classify these ‐structures up to elementary equivalence, and get in particular (...)
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  15.  90
    Science, Pseudoscience, and Science Falsely So-CaIIed.Daniel P. Thurs & Ronald L. Numbers - 2013 - In Massimo Pigliucci & Maarten Boudry (eds.), Philosophy of Pseudoscience: Reconsidering the Demarcation Problem. University of Chicago Press. pp. 121.
    This chapter presents a historical analysis of pseudoscience, tracking down the coinage and currency of the term and explaining its shifting meaning in tandem with the emerging historical identity of science. The discussions cover the invention of pseudoscience; science and pseudoscience in the late nineteenth century; pseudoscience in the new century; and pseudoscience and its critics in the late twentieth century.
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  16. True Beauty.Ryan P. Doran - forthcoming - British Journal of Aesthetics.
    What is the nature of the concept BEAUTY? Does it differ fundamentally from nearby concepts such as PRETTINESS? It is argued that BEAUTY, but not PRETTINESS, is a dual-character concept. Across a number of contexts, it is proposed that BEAUTY has a descriptive sense that is characterised by, inter alia, having intrinsically pleasing appearances; and a normative sense associated with deeply-held values. This account is supported across two, pre-registered, studies (N=500), and by drawing on analysis of corpus data. It is (...)
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  17.  96
    Freedom, Harmony & Moral Beauty.Ryan P. Doran - forthcoming - Philosophers' Imprint.
    Why are moral actions beautiful, when indeed they are? This paper assesses the view, found most notably in Schiller, that moral actions are beautiful just when they present the appearance of freedom by appearing to be the result of internal harmony (the Schillerian Internal Harmony Thesis). I argue that while this thesis can accommodate some of the beauty involved in contrasts of the ‘continent’ and the ‘fully’ virtuous, it cannot account for all of the beauty in such contrasts, and so (...)
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  18.  9
    Experimental Philosophy and the Philosophical Tradition.Stephen Stich & Kevin P. Tobia - 2016 - In Justin Sytsma & Wesley Buckwalter (eds.), A Companion to Experimental Philosophy. Malden, MA: Wiley. pp. 3–21.
    Many experimental philosophers are philosophers by training and professional affiliation, but some best work in experimental philosophy has been done by people who do not have advanced degrees in philosophy and do not teach in philosophy departments. This chapter explains that the experimental philosophy is the empirical investigation of philosophical intuitions, the factors that affect them, and the psychological and neurological mechanisms that underlie them. It explores what are philosophical intuitions, and why do experimental philosophers want to study them using (...)
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  19. The adicity of 'believes' and the hidden indexical theory.P. Ludlow - 1996 - Analysis 56 (2):97-101.
  20.  30
    Fictionalism in Philosophy.Bradley P. Armour-Garb & Fred Kroon (eds.) - 2019 - Oxford, England: Oxford University Press.
    There are things we routinely say that may strike us as literally false but that we are nonetheless reluctant to give up. This might be something mundane, like the way we talk about the sun setting in the west, or it could be something much deeper, like engaging in talk that is ostensibly about numbers despite believing that numbers do not literally exist. Rather than regard such behaviour as self-defeating, a "fictionalist" is someone who thinks that this kind (...)
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  21.  11
    Treatise on the origin of humanity (Taishō volume 45, number 1886).John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi - 2017 - In John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi (eds.), Three short treatises by Vasubandhu, Sengzhao, and Zongmi. Moraga, California: BDK America.
  22. A Mahayana demonstration on the theme of action (Taishō volume 31, number 1609).John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi - 2017 - In John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi (eds.), Three short treatises by Vasubandhu, Sengzhao, and Zongmi. Moraga, California: BDK America.
  23.  6
    Essays of Sengzhao (Taishō volume 45, number 1858).John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi - 2017 - In John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi (eds.), Three short treatises by Vasubandhu, Sengzhao, and Zongmi. Moraga, California: BDK America.
  24. The numbers in italics refer to the pages on which the complete references are listed.R. P. Abeles, J. Adelson, A. Ahlgren, M. D. S. Ainsworth, G. W. Allport, R. Alpert, D. Anderson, M. Arnold, J. Aronfreed & Averill Jr - 1975 - In David J. DePalma & Jeanne M. Foley (eds.), Moral Development: Current Theory and Research. Halsted Press.
     
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  25.  20
    Knowledge, attitude and practice of medical ethics among medical intern students in a Medical College in Kathmandu.Ramesh P. Aacharya & Yagya L. Shakya - 2016 - Bangladesh Journal of Bioethics 6 (3):1-9.
    This baseline study was conducted to find out the knowledge, attitudes and practices of medical ethics among the undergraduate medical interns who did not have structured ethics curriculum in their course. A descriptive, cross-sectional study was carried out using a self-administered structured questionnaire among the medical undergraduate interns of Maharajgunj Medical Campus, the pioneer medical college of Nepal which enrols 60 students in a year. A total of 46 interns participated in the study. The most common source of knowledge on (...)
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  26.  8
    Сommunicative Discourse of Tattvasaṅgrāha by Śāntarakṣita.Vladimir P. Ivanov & Иванов Владимир Павлович - 2024 - RUDN Journal of Philosophy 28 (1):57-68.
    The study provides an insight into the structural features of the famous VIII century Buddhist treatise Tattvasaṅgrāha by Śāntarakṣita with regard to the text’s main purpose ( prayojana ) as it is treated in Kamalaśīla’s commentary Pañjikā. Any text along with its referential (representational) function of conveying message - meaning to the addressee, or its expressive function, reflecting the author's attitude to what is communicated, also performs the ‘appellative’ function, encouraging the recipient of the message to act. This function which (...)
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  27.  24
    Hobbes without Grotius.P. Zagorin - 2000 - History of Political Thought 21 (1):16-40.
    This essay presents a critique of current views of Hugo Grotius which erroneously see him as a major theorist of natural rights and a formative influence upon the rights theory of Thomas Hobbes. Especially singled out for criticism are the misconceptions due to Richard Tuck in a number of writings that discuss the political ideas of Grotius and Hobbes and the relationship between them. In an examination of Hobbes's conception of natural rights, the essay reaffirms its originality and notes its (...)
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  28.  42
    Complexity and post-modernism: understanding complex systems.P. Cilliers & David Spurrett - 1999 - South African Journal of Philosophy 18 (2):258-274.
    This is a review article of Paul Cillier's 1999 book _Complexity and Postmodernism_. The review article is generally encouraging and constructive, although isolates a number of areas in need of clarification or development in Cillier's work. The volume of the _South African Journal of Philosophy_ in which the review article appeared also printed a response by Cilliers.
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  29.  24
    Acoustic correlates of emotional dimensions in laughter: Arousal, dominance, and valence.Diana P. Szameitat, Chris J. Darwin, Dirk Wildgruber, Kai Alter & André J. Szameitat - 2011 - Cognition and Emotion 25 (4):599-611.
    Although laughter plays an essential part in emotional vocal communication, little is known about the acoustical correlates that encode different emotional dimensions. In this study we examined the acoustical structure of laughter sounds differing along four emotional dimensions: arousal, dominance, sender's valence, and receiver-directed valence. Correlation of 43 acoustic parameters with individual emotional dimensions revealed that each emotional dimension was associated with a number of vocal cues. Common patterns of cues were found with emotional expression in speech, supporting the hypothesis (...)
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  30.  25
    Constructive definition of certain analytic sets of numbers.P. Lorenzen & J. Myhill - 1959 - Journal of Symbolic Logic 24 (1):37-49.
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  31.  11
    Proceedings of the Second Conference on Artificial General Intelligence.B. Goertzel, P. Hitzler & M. Hutter (eds.) - 2009 - Atlantis Press.
    The Conference on Artificial General Intelligence is the only major conference series devoted wholly and specifically to the creation of AI systems possessing general intelligence at the human level and ultimately beyond. Its second installation, AGI-09, in Arlington, Virginia, March 6-9, 2009, attracted 67 paper submissions, which is a substantial increase from the previous year. Of these submissions, 33 (i.e., 49%) were accepted as full papers for presentation at the conference. Additional 13 papers were included as position papers. The program (...)
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  32.  13
    John of St. Thomas [Poinsot] on Sacred Science: Cursus Theologicus I, Question 1, Disputation 2.John P. Doyle & Victor M. Salas (eds.) - 2014 - South Bend, Indiana: St. Augustine's Press.
    This volume offers an English translation of John of St. Thomas's Cursus theologicus I, question I, disputation 2. In this particular text, the Dominican master raises questions concerning the scientific status and nature of theology. At issue, here, are a number of factors: namely, Christianity's continual coming to terms with the "Third Entry" of Aristotelian thought into Western Christian intellectual culture - specifically the Aristotelian notion of 'science' and sacra doctrina's satisfaction of those requirements - the Thomistic-commentary tradition, and the (...)
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  33.  38
    Philosophical Investigations.P. M. S. Hacker & Joachim Schulte (eds.) - 2009 - Wiley-Blackwell.
    Incorporating significant editorial changes from earlier editions, the fourth edition of Ludwig Wittgenstein's _Philosophical Investigations_ is the definitive _en face_ German-English version of the most important work of 20th-century philosophy The extensively revised English translation incorporates many hundreds of changes to Anscombe’s original translation Footnoted remarks in the earlier editions have now been relocated in the text What was previously referred to as ‘Part 2’ is now republished as _Philosophy of Psychology – A Fragment_, and all the remarks in it (...)
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  34.  5
    Constructive Definition of Certain Analytic Sets of Numbers.P. Lorenzen & J. Myhill - 1968 - Journal of Symbolic Logic 33 (2):295-295.
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  35. Squeezing arguments.P. Smith - 2011 - Analysis 71 (1):22-30.
    Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s one familiar example. When we start learning computability theory, we are introduced to the idea of an algorithmically computable function (...)
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  36. For pluralism and against realism about species.P. Kyle Stanford - 1995 - Philosophy of Science 62 (1):70-91.
    I argue for accepting a pluralist approach to species, while rejecting the realism about species espoused by P. Kitcher and a number of other philosophers of biology. I develop an alternative view of species concepts as divisions of organisms into groups for study which are relative to the systematic explanatory interests of biologists at a particular time. I also show how this conception resolves a number of difficult puzzles which plague the application of particular species concepts.
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  37.  3
    Do Good Games Make Good People?Brendan P. Shea - 2013-08-26 - In Kevin S. Decker (ed.), Ender's Game and Philosophy. Wiley. pp. 89–98.
    Ender Wiggin spends much of Ender's Game playing games of one sort or another. These range from simple role‐playing games with his siblings (“buggers and astronauts”), to battleroom contests, to the strange free play Giant's Drink video game in which he must kill a giant and confront his deepest fears. This chapter examines the role that games play in Ender's development as both a military commander and as a human being. It considers a number of interrelated questions: What is a (...)
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  38.  12
    Empirical research in bioethical journals. A quantitative analysis.P. Borry - 2006 - Journal of Medical Ethics 32 (4):240-245.
    Objectives: The objective of this research is to analyse the evolution and nature of published empirical research in the fields of medical ethics and bioethics.Design: Retrospective quantitative study of nine peer reviewed journals in the field of bioethics and medical ethics .Results: In total, 4029 articles published between 1990 and 2003 were retrieved from the journals studied. Over this period, 435 studies used an empirical design. The highest percentage of empirical research articles appeared in Nursing Ethics , followed by the (...)
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  39.  18
    Varieties of BL-Algebras II.P. Aglianò & F. Montagna - 2018 - Studia Logica 106 (4):721-737.
    In this paper we introduce a poset of subvarieties of BL-algebras, whose completion is the entire lattice of subvarietes; we exhibit also a description of this poset in terms of finite sequences of functions on the natural numbers.
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  40.  39
    Emotion, moral perception, and nursing practice.P. Anne Scott - 2000 - Nursing Philosophy 1 (2):123-133.
    Many of the activities of clinical practice happen to, with or upon vulnerable human beings. For this reason numerous nursing authors draw attention to or claim a significant moral domain in clinical practice. A number of nursing authors also discuss the emotional involvement and/or emotional labour which is often experienced in clinical practice. In this article I explore the importance of emotion for moral perception and moral agency. I suggest that an aspect of being a good nurse is having an (...)
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  41.  20
    Representation, reasoning, and relational structures: a hybrid logic manifesto.P. Blackburn - 2000 - Logic Journal of the IGPL 8 (3):339-365.
    This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad.In essence, modal logic is a simple formalism for working with relational structures . But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference to (...)
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  42.  77
    Ultimate truth vis- à- vis stable truth.P. D. Welch - 2008 - Review of Symbolic Logic 1 (1):126-142.
    We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: (...)
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  43.  35
    Discussion. How to weight scientists' probabilities is not a big problem: Comment on Barnes.P. E. Meehl - 1999 - British Journal for the Philosophy of Science 50 (2):283-295.
    Assuming it rational to treat other persons' probabilities as epistemically significant, how shall their judgements be weighted (Barnes [1998])? Several plausible methods exist, but theorems in classical psychometrics greatly reduce the importance of the problem. If scientists' judgements tend to be positively correlated, the difference between two randomly weighted composites shrinks as the number of judges rises. Since, for reasons such as representative coverage, minimizing bias, and avoiding elitism, we would rarely employ small numbers of judges (e.g. less than (...)
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  44.  63
    Cell decomposition for P‐minimal fields.Marie-Hélène Mourgues - 2009 - Mathematical Logic Quarterly 55 (5):487-492.
    In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p-adically closed fields. We work here with the notion of P-minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8].
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  45. Utilitarianism and Distributive Justice: The Civil Law and the Foundations of Bentham's Economic Thought*: P. J. Kelly.P. J. Kelly - 1989 - Utilitas 1 (1):62-81.
    Between 1787, and the end of his life in 1832, Bentham turned his attention to the development and application of economic ideas and principles within the general structure of his legislative project. For seventeen years this interest was manifested through a number of books and pamphlets, most of which remained in manuscript form, that develop a distinctive approach to economic questions. Although Bentham was influenced by Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, he (...)
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  46.  38
    Do school-age children remember or know the personal past?P. Piolino, M. Hisland, I. Ruffeveille, V. Matuszewski, I. Jambaqué & F. Eustache - 2007 - Consciousness and Cognition 16 (1):84-101.
    The aim of this study was to examine developmental differences in autobiographical memory using a novel test that assesses its semantic and episodic subcomponents. Forty-two children aged 7–13 years were asked to recall semantic information and episodic events from three different time periods. For the recalls of all events, sense of remembering or sense of just knowing was measured via the Remember/Know paradigm. Age-related differences were observed for episodic autobiographical memory whereas semantic autobiographical memory was characterized by a relative developmental (...)
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  47.  56
    Identity and probability in Everett's multiverse.P. Tappenden - 2000 - British Journal for the Philosophy of Science 51 (1):99-114.
    There are currently several versions of Everett's relative state interpretation of quantum mechanics, responding to a number of perceived problems for the original proposal. One of those problems is whether Everett's idea is in accord with the standard 'probabilistic' interpretation implicit in the Born rule. I argue in defence of what appears to be Everett's original view on this. The contribution I aim to make is a more complete discussion of the central issues of the identity of objects and observers (...)
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  48.  15
    On chromatic number of graphs and set systems.P. Erdös, A. Hajnal & B. Rothchild - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 531--538.
  49. Operational analysis.P. W. Bridgman - 1938 - Philosophy of Science 5 (2):114-131.
    In the October 1937 number of Philosophy of Science Lindsay has made certain criticisms of the adequacy of the “operational method” of analyzing and giving meaning to the concepts of physics, documenting his criticisms chiefly from my own writings. In these criticisms he has made statements as to the method which I would by no means accept. This is not characteristic of his paper only, for I have seldom indeed seen a printed discussion of the method which I would accept (...)
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  50.  91
    Should Zelen pre-randomised consent designs be used in some neonatal trials?P. Allmark - 1999 - Journal of Medical Ethics 25 (4):325-329.
    My aim is to suggest that there is a case for using a randomised consent design in some neonatal trials. As an example I use the trials of extracorporeal membrane oxygenation (ECMO) in neonates suffering pulmonary hypertension. In some trials the process of obtaining consent has the potential to harm the subject, for example, by disappointing those who end in the control group and by creating additional anxiety at times of acute illness. An example of such were the trials of (...)
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