Search results for 'O. Hamilton' (try it on Scholar)

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  1.  20
    Alastair Hamilton (2011). Encounters with a Radical Erasmus: Erasmus' Work as a Source of Radical Thought in Early Modern Europe. By Peter G. Bietenholz, Exploiting Erasmus: The Erasmian Legacy and Religious Change in Early Modern England. By Gregory D. Dodds and Paraphrases on the Epistles to the Cortinthians, Ephesians, Philippians, Colossians, and Thessalonians. By Desiderius Erasmus [Collected Works of Erasmus, Vol. 43]. Edited by Robert D. Sider. Translated and Annotated by Mechtilde O'Mara and Edward A. Phillips Jr. [REVIEW] Heythrop Journal 52 (3):500-501.
  2.  7
    W. Hamilton (1933). Greek Astronomy. By Sir Thomas Heath, K.C.B., K.C.V.O. Pp. Lv + 192. (The Library of Greek Thought.) London: Dent, 1932. Cloth, 5s. [REVIEW] The Classical Review 47 (02):84-85.
  3.  17
    Alastair Hamilton (2007). Malleus Maleficarum. By Henricus Institoris, O. P. And Jacobus Sprenger, O. P. Edited and Translated by Christopher S. MacKay, Heresy, Magic, and Witchcraft in Early Modern Europe. By Gary K. Waite and Demonic Possession and Exorcism in Early Modern France. By Sarah Ferber. [REVIEW] Heythrop Journal 48 (3):477–479.
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  4.  2
    J. W. Hamilton (1986). Eugene O'Neill and Addison's Disease. Perspectives in Biology and Medicine 30 (2):231-234.
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  5.  2
    Andrew Hamilton (2007). The Convergence of Theology: A Festscrift Honoring Gerald O'Collins, S.J. [Book Review]. The Australasian Catholic Record 84 (2):246.
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  6. Christopher Hamilton (2007). The Christian Platonism of Simone Weil, Edited by E. Jane Doering and Eric O. Springsted. [REVIEW] Ars Disputandi 7.
     
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  7.  12
    Daniel Gibson, Benders G., A. Gwynedd, Cynthia Andrews-Pfannkoch, Evgeniya Denisova, Baden-Tillson A., Zaveri Holly, Stockwell Jayshree, B. Timothy, Anushka Brownley, David Thomas, Algire W., A. Mikkel, Chuck Merryman, Lei Young, Vladimir Noskov, Glass N., I. John, J. Craig Venter, Clyde Hutchison, Smith A. & O. Hamilton (2008). Complete Chemical Synthesis, Assembly, and Cloning of a Mycoplasma Genitalium Genome. Science 319 (5867):1215--1220.
    We have synthesized a 582,970-base pair Mycoplasma genitalium genome. This synthetic genome, named M. genitalium JCVI-1.0, contains all the genes of wild-type M. genitalium G37 except MG408, which was disrupted by an antibiotic marker to block pathogenicity and to allow for selection. To identify the genome as synthetic, we inserted "watermarks" at intergenic sites known to tolerate transposon insertions. Overlapping "cassettes" of 5 to 7 kilobases (kb), assembled from chemically synthesized oligonucleotides, were joined by in vitro recombination to produce intermediate (...)
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  8. David Hamilton, Glen Atkinson, William M. Dugger & William T. Waller Jr (eds.) (2009). Cultural Economics and Theory: The Evolutionary Economics of David Hamilton. Routledge.
    David Hamilton is a leader in the American institutionalist school of heterodox economics that emerged after WWII. This volume includes 25 articles written by Hamilton over a period of nearly half a century. In these articles he examines the philosophical foundations and practical problems of economics. The result of this is a unique institutionalist view of how economies evolve and how economics itself has evolved with them. Hamilton applies insight gained from his study of (...)
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  9. Kang-nam O. (2011). Chonggyo, Simch'ŭng Ŭl Poda: O Kang-Nam Kyosu Ka Mannan Yŏngsŏng Ŭi Kŏindŭl. Hyŏnamsa.
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  10.  6
    H. Williamson (1926). Some School Books Latin Reader for Secondary Schools. By D. E. Hamilton and J. O. Carlisle. Pp. 1–319. Harrap and Co. 3s. 6d. [REVIEW] The Classical Review 40 (05):158-.
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  11. Norberto M. Ibáñez (2007). El futuro en sus manos: Entrevista a Hamilton O. Smith, Marchal W. Nirenberg, Mario J. Molina, Edmond H. Fischer y Werner Arber. [REVIEW] Contrastes: Revista Cultural 49:29-39.
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  12.  9
    Amitrajeet A. Batabyal (2001). J. B. Braden and S. Proost, Editors, the Economic Theory of Environmental Policy in a Federal System; A. Cornwell and J. Creedy, Environmental Taxes and Economic Welfare; G. Atkinson, R. Dubourg, K. Hamilton, M. Munasinghe, D. Pearce, and C. Young, Measuring Sustainable Development: Macroeconomics and the Environment; R. Nau, E. Gronn, M. Machina, and O. Bergland, Editors, Economic and Environmental Risk and Uncertainty: New Models and Methods. [REVIEW] Journal of Agricultural and Environmental Ethics 14 (1):97-103.
  13. Michael Crowe (1985). William Rowan Hamilton: Portrait of a Prodigy by Sean O'Donnell. [REVIEW] Isis: A Journal of the History of Science 76:47-448.
     
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  14. Jonathan Birch (2014). Hamilton's Rule and Its Discontents. British Journal for the Philosophy of Science 65 (2):381-411.
    In an incendiary 2010 Nature article, M. A. Nowak, C. E. Tarnita, and E. O. Wilson present a savage critique of the best-known and most widely used framework for the study of social evolution, W. D. Hamilton’s theory of kin selection. More than a hundred biologists have since rallied to the theory’s defence, but Nowak et al. maintain that their arguments ‘stand unrefuted’. Here I consider the most contentious claim Nowak et al. defend: that Hamilton’s rule, (...)
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  15.  12
    John O'Neill (1986). Formalism, Hamilton and Complex Numbers. Studies in History and Philosophy of Science Part A 17 (3):351-372.
    The development and applicability of complex numbers is often cited in defence of the formalist philosophy of mathematics. This view is rejected through an examination of hamilton's development of the notion of complex numbers as ordered pairs of reals, And his later development of the quaternion theory, Which subsequently formed the basis of vector analysis. Formalism, By protecting informal assumptions from critical scrutiny, Constrained rather than encouraged the development of mathematics.
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  16. Oleg Belegradek, Ya'Acov Peterzil & Frank Wagner (2000). Quasi-o-Minimal Structures. Journal of Symbolic Logic 65 (3):1115-1132.
    A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...)
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  17.  58
    Graham Oppy (2010). The Shape of Causal Reality: A Naturalistic Adaptation of O’Connor’s Cosmological Argument. Philosophia Christi 12 (2):281-288.
    This paper is a companion to an article that I published in *Oxford Studies in Philosophy of Religion*. The OSPR discusses the third chapter of Tim O'Connor's *Theism and Ultimate Explanation. This paper discusses a range of other issues that are not picked up in the OSPR discussion.
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  18.  10
    Abraham H. Gibson (2013). Edward O. Wilson and the Organicist Tradition. Journal of the History of Biology 46 (4):599-630.
    Edward O. Wilson’s recent decision to abandon kin selection theory has sent shockwaves throughout the biological sciences. Over the past two years, more than a hundred biologists have signed letters protesting his reversal. Making sense of Wilson’s decision and the controversy it has spawned requires familiarity with the historical record. This entails not only examining the conditions under which kin selection theory first emerged, but also the organicist tradition against which it rebelled. In similar fashion, one must not only examine (...)
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  19.  47
    John Corcoran (2007). The principle of wholistic reference/o princípio da referência universalista. Manuscrito 30 (2):493-505.
    In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...)
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  20.  48
    Graham Oppy (2011). O'Connor's Cosmological Argument. Oxford Studies in Philosophy of Religion: Vol. 3 3:166.
    This chapter is a critical discussion of the third chapter of Tim O'Connor's *Theism and Ultimate Explanation*. In this chapter, O'Connor advances the "existence stage" of his cosmological argument from contingency. I argue that naturalists have good reason to think that on each of the live hypotheses--infinite regress, brute contingency, brute necessity--naturalism is preferable to theism.
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  21. Thomas M. Besch (2008). Constructing Practical Reason: O'Neill on the Grounds of Kantian Constructivism. Journal of Value Inquiry 42 (1):55-76.
    The paper addresses O'Neill's view that her version of Kant's Categorical Imperative, namely, the requirement of followability (RF), marks the supreme principle of reason; it takes issue with her claim that RF commits us to Kantian constructivism in practical philosophy. The paper distinguishes between two readings of RF: on a weak reading, RF ranges over all (practical) reasoning but does not commit to constructivism, and on a strong version RF commits to constructivism but fails to meet its own test, and (...)
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  22.  2
    Jafar S. Eivazloo & Somayyeh Tari (forthcoming). SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures. Notre Dame Journal of Formal Logic.
    Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong CE-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has SCE-cell decomposition if and only if its canonical o-minimal extension has CE-cell decomposition. Then, we show that every weakly o-minimal structure with SCE-cell decomposition satisfies OCP. Our last result implies that every o-minimal structure in which every definable open (...)
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  23.  13
    Carlo Toffalori & Kathryn Vozoris (2009). Notes on Local o‐Minimality. Mathematical Logic Quarterly 55 (6):617-632.
    We introduce and study some local versions of o-minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions.
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  24.  38
    Alexander Gersten (2011). Tensor Lagrangians, Lagrangians Equivalent to the Hamilton-Jacobi Equation and Relativistic Dynamics. Foundations of Physics 41 (1):88-98.
    We deal with Lagrangians which are not the standard scalar ones. We present a short review of tensor Lagrangians, which generate massless free fields and the Dirac field, as well as vector and pseudovector Lagrangians for the electric and magnetic fields of Maxwell’s equations with sources. We introduce and analyse Lagrangians which are equivalent to the Hamilton-Jacobi equation and recast them to relativistic equations.
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  25.  8
    David Duarte (2015). Analogija i vaganje: teza o djelomičnoj svodljivosti i njezini problemi. Revus 25:127-140.
    Na temelju analize strukture i slijeda postupka analogije, autor upućuje kritiku tezi o djelomičnoj svodljivosti, tj. tezi prema kojoj se analogija, izuzev onoga njezinog koraka koji predstavlja strogu analogiju, može svesti na vaganje. U radu se stoga prvo iznose neki problemi navedene teze, poput nenužnosti svodljivosti ili činjenice da se pod krinkom vaganja provodi prava analogija. Središnja je teza rada tvrdnja da analogiju nije moguće uspješno svesti na oblik vaganja.
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  26.  30
    Vincent W. J. Van Gerven Oei (2012). Cumposition: Theses on Philosophy's Etymology. Continent 2 (1).
    continent. 2.1 (2012): 44–55. Philosophers are sperm, poetry erupts sperm and dribbles, philosopher recodes term, to terminate, —A. Staley Groves 1 There is, in the relation of human languages to that of things, something that can be approximately described as “overnaming”—the deepest linguistic reason for all melancholy and (from the point of view of the thing) for all deliberate muteness. Overnaming as the linguistic being of melancholy points to another curious relation of language: the overprecision that obtains in the tragic (...)
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  27.  26
    C. D. Bailey (2004). Hamilton and the Law of Varying Action Revisited. Foundations of Physics 34 (9):1385-1406.
    According to history texts, philosophers searched for a unifying natural law whereby natural phenomena and numbers are related. More than 2300 years ago, Aristotle postulated that nature requires minimum energy. More than 220 years ago, Euler applied the minimum energy postulate. More than 200 years ago, Lagrange provided a mathematical “proof” of the postulate for conservative systems. The resulting Principle of Least Action served only to derive the differential equations of motion of a conservative system. Then, 170 years ago, (...) presented what he claimed to be a “general method in dynamics.” Hamilton's resulting “Law of Varying Action” was supposed to apply to both conservative and non-conservative systems and was supposed to yield either the differential equations of motion or the integrals of those differential equations. However, no direct evaluation of the integrals of motion ever resulted from Hamilton's law of varying action. In 1975, a scant 29 years ago, following five years of controversy with engineer mechanicians, Dr. Wolfgang Yourgrau, Editor, Foundations of Physics, published my first paper based on Aristotle's postulate, without mathematical proof. That and subsequent papers present, through applications, a true “general method in dynamics.” In this essay, I present the mathematical proof that is missing from my 1975 and subsequent papers. Six fundamental integrals of analytical mechanics are derived from Aristotle's postulate. First, however, Hamilton must be revisited to show why his H function and his “force function” prevents the law of varying action from being the general method in dynamics that he claimed it to be. I have found that Hamilton’s Law of Varying Action (HLVA), as Hamilton presented it, cannot be applied to systems for which the force function is non-integrable. In 1972, Dr. B.E. Gatewood and Dr. D.P. Beres (then a graduate student) discovered that the end-point term associated with the principle of least action does not vanish. I named the new equation, “the general energy equation.” In 1973, because I was doing with it what Hamilton claimed could be done with HLVA, I simply assumed that this new equation was HLVA. I gave the new equation the misnomer HLVA. In 2001, I learned that I had made a grave mistake. I found that HLVA is at most a special case of the general energy equation. My interpretation of Aristotle's postulate permits one to by-pass the differential equations of motion completely for both conservative and non-conservative systems (no calculus of variations). (shrink)
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  28. Paul Thompson (ed.) (1995). Issues in Evolutionary Ethics. State University of New York Press.
    This book explores historical and current discussions of the relevance of evolutionary theory to ethics. The historical section conveys the intellectual struggle that took place within the framework of Darwinism from its inception up to the work of G. C. Williams, W. D. Hamilton, R. D. Alexander, A. L. Trivers, E. O. Wilson, R. Dawkins, and others. The contemporary section discusses ethics within the framework of evolutionary theory as enriched by the works of biologists such as those (...)
     
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  29.  8
    Dugald Macpherson & Charles Steinhorn (1997). Extending Partial Orders on o‐Minimal Structures to Definable Total Orders. Mathematical Logic Quarterly 43 (4):456-464.
    It is shown that if is an o-minimal structure such that is a dense total order and ≾ is a parameter-definable partial order on M, then ≾ has an extension to a definable total order.
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  30.  72
    Daniel Howard-Snyder (2001). Review of David O'Connor, God and Inscrutable Evil. [REVIEW] Philosophical Review.
    This is a critical review of David O'Connor's book, God and Inscrutable Evil.
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  31.  5
    Mário J. Edmundo & Pantelis E. Eleftheriou (2007). The Universal Covering Homomorphism in o‐Minimal Expansions of Groups. Mathematical Logic Quarterly 53 (6):571-582.
    Suppose G is a definably connected, definable group in an o-minimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism equation image: equation image→ G is a locally definable covering homomorphism and π1 is isomorphic to the o-minimal fundamental group π of G defined using locally definable covering homomorphisms.
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  32.  73
    Robert Boyd & Peter Richerson (2006). Culture, Adaptation, and Innateness. In Peter Carruthers, Stephen Laurence & Stephen P. Stich (eds.), The Innate Mind: Culture and Cognition.
    It is almost 30 years since the sociobiology controversy burst into full bloom. The modern theory of the evolution of animal behavior was born in the mid 1960’s with Bill Hamilton’s seminal papers on inclusive fitness and George William’s book Adaptation and Natural Selection. The following decade saw an avalanche of important ideas on the evolution of sex ratio, animal conflicts, parental investment, and reciprocity, setting off a revolution our understanding of animal societies, a revolution that is still going (...)
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  33.  17
    Pantelis E. Eleftheriou (2009). Compact Domination for Groups Definable in Linear o-Minimal Structures. Archive for Mathematical Logic 48 (7):607-623.
    We prove the Compact Domination Conjecture for groups definable in linear o-minimal structures. Namely, we show that every definably compact group G definable in a saturated linear o-minimal expansion of an ordered group is compactly dominated by (G/G 00, m, π), where m is the Haar measure on G/G 00 and π : G → G/G 00 is the canonical group homomorphism.
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  34.  26
    Pantelis E. Eleftheriou (2013). Non-Standard Lattices and o-Minimal Groups. Bulletin of Symbolic Logic 19 (1):56-76.
    We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of pregeometry and (...)
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  35.  5
    Chris Miller & James Tyne (2006). Expansions of o-Minimal Structures by Iteration Sequences. Notre Dame Journal of Formal Logic 47 (1):93-99.
    Let P be the ω-orbit of a point under a unary function definable in an o-minimal expansion ℜ of a densely ordered group. If P is monotonically cofinal in the group, and the compositional iterates of the function are cofinal at +\infty in the unary functions definable in ℜ, then the expansion (ℜ, P) has a number of good properties, in particular, every unary set definable in any elementarily equivalent structure is a disjoint union of open intervals and finitely many (...)
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  36.  10
    A. Arensburg & L. P. Horwitz (1992). A First-Order Equation for Spin in a Manifestly Relativistically Covariant Quantum Theory. Foundations of Physics 22 (8):1025-1039.
    Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time τ. The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector nμ; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous study (...)
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  37.  7
    Mário J. Edmundo & Pantelis E. Eleftheriou (2009). Definable Group Extensions in Semi‐Bounded o‐Minimal Structures. Mathematical Logic Quarterly 55 (6):598-604.
    In this note we show: Let R = 〈R, <, +, 0, …〉 be a semi-bounded o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m . Then G is a definable extension of a bounded definable group B by 〈Rm, +〉.
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  38.  14
    Philippe Choquard (2001). The Homogeneous Hamilton–Jacobi and Bernoulli Equations Revisited. Foundations of Physics 31 (4):623-640.
    The one-dimensional case of the homogeneous Hamilton–Jacobi and Bernoulli equations St $${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0em}\!\lower0.7ex\hbox{$2$}}$$ S x 2 =0, where S(x, t) is Hamilton's principal function of a free particle and also Bernoulli's momentum potential of a perfect liquid, is considered. Non-elementary solutions are looked for in terms of odd power series in t with x-dependent coefficients and even power series in x with t-dependent coefficients. In both cases, and depending upon initial conditions, unexpected regularities are observed (...)
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  39.  10
    Janak Ramakrishnan (2010). Uniform Bounds on Growth in o-Minimal Structures. Mathematical Logic Quarterly 56 (4):406-408.
    We prove that a function definable with parameters in an o-minimal structure is bounded away from ∞ as its argument goes to ∞ by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in [1]. Moreover, this remains true if the argument is taken to approach any element of the structure , and the function has limit any element of the structure.
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  40.  24
    Gerald A. Cory (2002). Maclean's Evolutionary Neuroscience, the Csn Model and Hamilton's Rule: Some Developmental, Clinical, and Social Policy Implications. [REVIEW] Brain and Mind 3 (1):151-181.
    Paul MacLean, founder and long-time chief ofthe Laboratory of Brain Evolution and Behavior,National Institutes of Health, is a pioneeringfigure in the emergent field of evolutionaryneuroscience. His influence has been widelyfelt in the development of biologicalpsychiatry and has led to a considerableliterature on evolutionary approaches toclinical issues. MacLean's work is alsoenjoying a resurgence of interest in academicareas of neuroscience and evolutionarypsychology which have previously shown littleinterest or knowledge of his extensive work. This chapter builds on MacLean's work to bringtogether new insights (...)
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  41.  4
    Beibut Sh Kulpeshov (2011). Binary Types in ℵ0‐Categorical Weakly o‐Minimal Theories. Mathematical Logic Quarterly 57 (3):246-255.
    Orthogonality of all families of pairwise weakly orthogonal 1-types for ℵ0-categorical weakly o-minimal theories of finite convexity rank has been proved in 6. Here we prove orthogonality of all such families for binary 1-types in an arbitrary ℵ0-categorical weakly o-minimal theory and give an extended criterion for binarity of ℵ0-categorical weakly o-minimal theories . © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  42.  6
    Hassan Sfouli (2010). Definability and Nondefinability Results for Certain o-Minimal Structures. Mathematical Logic Quarterly 56 (5):503-507.
    The main goal of this note is to study for certain o-minimal structures the following propriety: for each definable C∞ function g0: [0, 1] → ℝ there is a definable C∞ function g: [–ε, 1] → ℝ, for some ε > 0, such that g = g0 for all x ∈ [0, 1].
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  43.  4
    Lélio Moura Lourenço & Luciana Xavier Senra (2012). A Violência Familiar Como Fator de Risco Para o Bullying Escolar: Contexto E Possibilidades de Intervenção. Aletheia 37:42-56.
    A violência doméstica (VD) ou familiar afeta a população mundial prejudicando a saúde, liberdade e bem-estar de indivíduos, famílias e comunidades. O bullying, um tipo de violência escolar, envolve comportamentos agressivos intencionais e repetitivos, físicos e psicológicos entre pares, visando prej..
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  44.  6
    Janak Ramakrishnan (2010). Maximal Small Extensions of o-Minimal Structures. Mathematical Logic Quarterly 56 (5):470-474.
    A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small extension. Our construction yields such a structure for any cardinality. We show that in some cases, notably when the base structure is countable, the maximal small extension has maximal possible cardinality.
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  45.  17
    Edward O. Wilson, Stephen J. Pope & Philip Hefner (2001). E. O. Wilson, Stephen Pope, and Philip Hefner: A Conversation. Zygon 36 (2):249-253.
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  46.  5
    Stefano Leonesi & Carlo Toffalori (2004). On the Boolean Algebras of Definable Sets in Weakly o‐Minimal Theories. Mathematical Logic Quarterly 50 (3):241-248.
    We consider the sets definable in the countable models of a weakly o-minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic , in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within (...)
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  47.  11
    Pantelis E. Eleftheriou (2010). Groups Definable in Linear o-Minimal Structures: The Non-Compact Case. Journal of Symbolic Logic 75 (1):208-220.
    Let $\scr{M}=\langle M,+,<,0,S\rangle $ be a linear o-minimal expansion of an ordered group, and $G=\langle G,\oplus ,e_{G}\rangle $ an n-dimensional group definable in $\scr{M}$ . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ${\ssf V}\text{-definable}$ subgroup U of $\langle M^{n},+\rangle $ and a lattice L of rank equal to the dimension of the 'compact part' of G.
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  48.  3
    S. Leonesi & Carlo Toffalori (2003). Omega-Categorical Weakly o-Minimal Expansions of Boolean Lattices. Mathematical Logic Quarterly 49 (4):394.
    We study ω-categorical weakly o-minimal expansions of Boolean lattices. We show that a structure [MATHEMATICAL SCRIPT CAPITAL A] = expanding a Boolean lattice by a finite sequence I of ideals of A closed under the usual Heyting algebra operations is weakly o-minimal if and only if it is ω-categorical, and hence if and only if A/I has only finitely many atoms for every I ∈ ℐ. We propose other related examples of weakly o-minimal ω-categorical models in this framework, and we (...)
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    Marcello Mamino (2011). Splitting Definably Compact Groups in o-Minimal Structures. Journal of Symbolic Logic 76 (3):973 - 986.
    An argument of A. Borel [Bor—61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.
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  50.  3
    A. Fornasiero & E. Vasquez Rifo (2012). Hausdorff Measure on o-Minimal Structures. Journal of Symbolic Logic 77 (2):631-648.
    We introduce the Hausdorff measure for definable sets in an o-minimal structure, and prove the Cauchy—Crofton and co-area formulae for the o-minimal Hausdorff measure. We also prove that every definable set can be partitioned into “basic rectifiable sets”, and that the Whitney arc property holds for basic rectifiable sets.
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